1. The price of the sugar rise by 25%. If a family wants to keep their expenses on sugar the same as earlier, the family will have to decrease its consumption of sugar by
a) 25%
b) 20%
c) 80%
d) 75%
Discussion
Explanation: Let the initial expenses on Sugar was Rs. 100.
Now, Price of Sugar rises 25%. So, to buy same amount of Sugar, they need to expense,
= (100 + 25% of 100) = Rs. 125.
But, They want to keep expenses on Sugar, so they have to cut Rs. 25 in the expenses to keep it to Rs. 100.
% decrease in Consumption,
$$\frac{{25}}{{125}} \times 100 = 20\% $$
2. P is 6 times greater than Q then by what per cent is Q smaller than P?
a) 84%
b) 85.5%
c) 80%
d) 83.33%
Discussion
Explanation: Let Q = 10.
Then, P = 60.
Q is 50 less than P.
Q, % less than P = $$\frac{{50}}{{60}} \times 100 = 83.33\% $$
3. In the recent, climate conference in New York, out of 700 men, 500 women, 800 children present inside the building premises, 20% of the men, 40% of the women and 10% of the children were Indians. Find the percentage of people who were not Indian?
a) 77%
b) 79%
c) 83%
d) 73%
Discussion
Explanation: Number of Indians men present there = $$\frac{{700 \times 20}}{{100}} = 140$$
Indian women = $$\frac{{500 \times 40}}{{100}} = 200$$
Indian children = $$\frac{{800 \times 10}}{{100}} = 80$$
Total member present in climate conference = 700 + 500 + 800 = 2000
Total Indian = 200 + 140 + 80 = 420
Hence, % of Indian present there = $$\frac{{420 \times 100}}{{2000}} = 21\% $$
% of people who were not Indian = 100 - 21 = 79%
4. If A's salary is 25% more than B's salary, then B's salary is how much lower than A's salary?
a) 20%
b) $$16\frac{2}{3}\% $$
c) $$33\frac{1}{3}\% $$
d) 25%
Discussion
Explanation: Let B's Salary is Rs. 100. Then,
A's Salary = (100 + 25% of 100) = Rs. 125
Difference between A's Salary and B's Salary = 125 - 100 = Rs. 25
% Difference (lower) = $$\frac{{25}}{{125}} \times 100 = 20\% $$
5. The population of a city is 35000. On an increase of 6% in the number of men and an increase of 4% in the number of women, the population would become 36760. What was the number of women initially?
a) 18000
b) 19000
c) 17000
d) 20000
Discussion
Explanation:
$$\eqalign{ & {\text{Let number of men in the population be }}x \cr & {\text{Number of women}} = \left( {35000 - x} \right) \cr & {\text{Increase in the number of men}} \cr & = 6\% \,of\,x = \frac{{6x}}{{100}} \cr & {\text{Increase in the number of women}} \cr & = \left( {3500 - x} \right) \times \frac{4}{{100}} \cr & {\text{Increase in whole population}} \cr & = 36760 - 35000 = 1760 \cr & \frac{{6x}}{{100}} + \left[ {\left( {35000 - x} \right) \times \frac{4}{{100}}} \right] = 1760 \cr & \left[ {\left( {6x - 4x} \right) + 35000 \times \frac{4}{{100}}} \right] = 1760 \cr & 2x + 35000 \times 4 = 1760 \times 100 \cr & 2x = 176000 - 35000 \times 4 \cr & x = 18000 \cr & {\text{Number}}\,{\text{of}}\,{\text{men}} = 18000 \cr & {\text{Number}}\,{\text{of}}\,{\text{women}} \cr & = 35000 - 18000 \cr & = 17000 \cr} $$
6. A and B are two fixed points 5 cm apart and C is a point on AB such that AC is 3cm. if the length of AC is increased by 6%, the length of CB is decreased by
a) 6%
b) 7%
c) 8%
d) 9%
Discussion
Explanation: As A and B are fixed, C is any point on AB, so if AC is increases then CB decreases.
A________3 cm_________ C _____2 cm____B
Then, solution can be visualized as,
Increase in AC 6% = $$\frac{{106 \times 3}}{{100}} = 3.18\,{\text{cm}}{\text{.}}$$
Decrease in CB = 0.18 cm
% decrease = $$\frac{{0.18}}{2} \times 100 = 9\% $$
7. An ore contains 25% of an alloy that has 90% iron. Other than this, in the remaining 75% of the ore, there is no iron. How many kilograms of the ore are needed to obtain 60 kg of pure iron?
a) 266.66 kg
b) 250 kg
c) 275 kg
d) 300 kg
Discussion
Explanation: Let there is 100 kg of ore.
25% ore contains 90% off Iron that means 25 kg contains;
$$\frac{{25 \times 90}}{{100}} = 22.5\,{\text{kg}}\,{\text{iron}}$$
22.5 kg Iron contains 100 kg of ore.
Then, 1 kg of iron contains = $$\frac{{25}}{{100}}{\text{kg}}\,{\text{ore}}$$
Hence, 60 kg iron contains
= $$\frac{{100 \times 60}}{{22.5}}$$
= 266.66 kg ore
8. Last year, the population of a town was x and if it increases at the same rate, next year it will be y. the present population of the town is
a) $$\frac{{x + y}}{2}$$
b) $$\frac{{2xy}}{{x + y}}$$
c) $$\sqrt {xy} $$
d) $$\frac{{y - x}}{2}$$
Discussion
Explanation:
$$\eqalign{ & {\text{Let the present population of the town be }}P \cr & {\text{Using compound interest formula}} \cr & {\text{Then}}, \cr & P = x\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right] - - - \,\left( i \right) \cr & {\text{And}}\,y = P\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right] \cr & = P \times \frac{P}{x} - - - - \,\left( {ii} \right) \cr & {P^2} = xy; \cr & {\text{Hence}},\,P = \sqrt {xy} \cr} $$
9. The length, breadth and height of a room in the shape of a cuboid are increased by 10%, 20% and 50% respectively. Find the percentage change in the volume of the cuboid.
a) 77%
b) 98%
c) 75%
d) 88%
Discussion
Explanation: Let each side of the cuboid be 10 unit initially.
Initial Volume of the cuboid,
= length * breadth * height = 10 × 10 × 10 = 1000 cubic unit.
After increment dimensions become,
Length = (10 + 10% of 10) = 11 unit.
Breadth = (10 + 20% of 10) = 12 unit.
Height = (10 + 50% of 10) = 15 unit.
Now, present volume = 11 × 12 × 15 = 1980 cubic unit.
Increase in volume = 1980 - 1000 = 980 cubic unit.
% increase in volume = $$\frac{{980}}{{1000}} \times 100 = 98\% $$
10. Population of a town increase 2.5% annually but is decreased by 0.5% every year due to migration. What will be the percentage increase in 2 years?
a) 5%
b) 4.04%
c) 4%
d) 3.96%
Discussion
Explanation: Net percentage increase in Population = (2.5 - 0.5) = 2% each year.
Let the Original Population of the town be 100.
Population of Town after 1 year = (100 + 2% of 100) = 102.
Population of the town after 2nd year = (102 + 2% of 102 ) = 104.04
Now, % increase in population = $$\frac{{4.04}}{{100}} \times 100 = 4.04\% $$
11. 30% of a number when subtracted from 91, gives the number itself. Find the number.
a) 60
b) 65
c) 70
d) 75
Discussion
Explanation: Let the number be x
According to the question,
91 - $$\frac{{30{\text{x}}}}{{100}}$$ = x
9100 - 30x = 100x
9100 = 130x
x = $$\frac{{9100}}{{130}}$$
Hence, x = 70
12. If two numbers are respectively 30% and 40% more than a third number, what percent is the first of the second?
a) 80%
b) $$92\frac{6}{7}\% $$
c) 75%
d) $$84\frac{4}{5}\% $$
Discussion
Explanation: Let the third number be 100. Then,
1st number = 130
2nd number = 140
% 1st number to the 2nd number
$$\eqalign{ & = \frac{{130 \times 100}}{{140}} \cr & = \frac{{650}}{7} \cr & = 92\frac{6}{7}\% \cr} $$
13. Each side of a rectangular field diminished by 40%. By how much per cent is the area of the field diminished?
a) 64%
b) 25%
c) 32%
d) 16%
Discussion
Explanation: Let the Original length of the rectangle be 20 unit and breadth be 10 unit. Then
Original Area = length *breadth = 20*10 = 200 Square unit.
40% decrease in each side, then
Length = (20 - 40% of 20) = 12 unit.
Breadth = (10 - 40% of 10) = 6 unit.
Now, Area = 12 × 6 = 72 Square unit.
Decrease in area = 200 - 72 = 128 square unit.
% Decrease in Area = $$\frac{{128}}{{200}} \times 100 = 64\% $$
14. Narayan spends 30% of his income on education and 50% of the remaining on food. He gives Rs. 1000 as monthly rent and now has Rs. 1800 left with him. What is his monthly income?
a) Rs. 7000
b) Rs. 8000
c) Rs. 6000
d) Rs. 9000
Discussion
Explanation: Narayan's saving and rent = 1000 + 1800 = Rs. 2800
Let his monthly income be Rs. 100
30% of his income he spent on education i.e. Rs. 30
Remaining = 100 - 30 = 70
50% of remaining on food = $$\frac{{70 \times 50}}{{100}} = {\text{Rs}}{\text{. 35}}$$
Now, that 35 must be equal to his saving and rent i.e.
35 = 2800 then,
1 = $$\frac{{2800}}{{35}}$$
100 = $$\frac{{2800 \times 100}}{{35}} = {\text{Rs}}{\text{. 8000}}$$
So, his income = Rs. 8000
15. The price of rice falls by 20%. How much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously?
a) 5 kg
b) 15 kg
c) 30 kg
d) 25 kg
Discussion
Explanation: Let Rs. 100 be spend on rice initially for 20 kg.
As the price falls by 20%, new price for 20 kg rice,
= (100 - 20% of 100) = 80
New price of rice = $$\frac{{80}}{{20}}$$ = Rs. 4 per kg.
Rice can bought now at = $$\frac{{100}}{{4}}$$ = 25 kg.
16. The cost of an article was Rs.75. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the article is:
a) Rs. 72
b) Rs. 60
c) Rs. 76
d) Rs. 75
Discussion
Explanation: Initial Cost = Rs. 75
After 20% increase in the cost, it becomes,
(75 + 20% of 75) = Rs. 90
Now, Cost is decreased by 20%, So cost will become,
(90 - 20% of 90) = Rs. 72
So, present cost is Rs. 72
17. Vicky's salary is 75% more than Ashu's. Vicky got a raise of 40% on his salary while Ashu got a raise of 25% on his salary. By what percent is Vicky's salary more than Ashu's?
a) 51.1%
b) 90%
c) 96%
d) 52.1%
Discussion
Explanation: Let Ashu's salary = 100; Ashu's salary after rise = 125
Then Vicky's salary = 175
Vicky's salary after rise of 40% = 245
[As 10% of Vicky's salary is 17.5 then 40% = 17.5 × 4 = 70]
Difference between Vicky's salary and Ashu's salary = 245 - 125 = 120
% more Vicky's salary than Ashu's = $$\frac{{120 \times 100}}{{125}} = 96\% $$
18. In an election between two candidates, the winner got 65% of the total votes cast and won the election by a majority of 2748 votes. What is the total number of votes cast if no vote is declared invalid?
a) 8580
b) 8720
c) 9000
d) 9160
Discussion
Explanation: Winner gets 65% of valid votes and loser gets 35% of votes
Difference between this two = 2748
(65-35)% = 2748
30% = 2748
Total number of voters, 100%
= $$\frac{{2748 \times 100}}{{30}}$$
= 9160
19. The population of village is 1,00,000. The rate of increase is 10% per annum. Find the population at the start of the third year?
a) 1,33,100
b) 1,21,000
c) 1,18,800
d) 1,20,000
Discussion
Explanation: 100000 == 10%↑(1st year) ==> 110000 == 10%↑(2nd year) ==> 121000
Population at starting of 3rd year = 121000
20. If the price of a commodity is decreased by 20% and its consumption is increased by 20%, what will be the increase or decrease in expenditure on the commodity?
a) 4% increase
b) 4% decrease
c) 8% increase
d) 8% decrease
Discussion
Explanation: Let the initial expenditure on the commodity be Rs. 100.
Now, the price decreases by 20%,
Current Price = (100 - 20% of 100) = Rs. 80.
Same time due to decrements in price 20% consumption has been increased. So,
Current expenses on commodity = (80 + 20% of 80)= Rs. 96.
Here, the initial expenditure was Rs. 100 which became 96 at the end, it means there is 4% decrements in the expenditure of the commodity.
21. 80% of a number added to 80 gives the result as the number itself, then the number is :
a) 200
b) 300
c) 400
d) 480
Discussion
Explanation: Let X be the number which is added to 80
80% of X = 0.8X
80 + 0.8X = X
0.2X = 80
X = $$\frac{{80}}{{0.2}} = 400$$
22. Reena goes to a shop to buy a radio costing Rs. 2568. The rate of sales tax is 7% and the final value is rounded off to the next higher integer. She tells the shopkeeper to reduce the price of the radio so that she has to pay Rs. 2568 inclusive of sales tax. Find the reduction needed in the price of the radio.
a) Rs. 180
b) Rs. 210
c) Rs. 168
d) Rs. 170
Discussion
Explanation:
$$\eqalign{ & {\text{Reduction}} \cr & = {\frac{7}{{107}}} \times 2568 \cr & = 168 \cr} $$
23. Australia scored a total of X runs in 50 overs. India tied the scores in 20% less overs. If India's average run rate had been 33.33% higher the scores would have been tied 10 overs earlier. Find how many runs were scored by Australia?
a) 250
b) 240
c) 200
d) Can't be determined
Discussion
Explanation: Run scored = Over × Run rate
If overs is reduced by 25%, run rate will go up by 33.33%. Hence, Australia could have scored any number of runs.
24. In 2000, the market shares of the toilet soaps Margo, Palmolive and dove were 40%, 30% and 30% respectively. Starting from the next year, a new soap enters into the market each year and gets 10% of the market share. The existing soap share the remaining market share in the same ratio as they did in the previous year. What percent of the total market share will mango have in 2002?
a) 28%
b) 32%
c) 32.4%
d) 34
Discussion
Explanation: In 2000, the market share was 40%, 30% and 30%, means
the ratio is 4 : 3 : 3
In 2001, a new product (A) enters and has 10% market share, 90% of the remaining market is shared by the previous 3.
Now, divide 90% in the ratio 4 : 3 : 3 , i.e 36%, 27%, 27%.
Now the ratio is 36 : 27 : 27 : 10
In 2002, another new product (B) enters and has 10% market share, now the remaining 90% market share is distributed in the ratio,
36 : 27 : 27 : 10
and hence remaining 32.4%, 24.3%, 24.3%, 9%
Thus, the market share of Margo in 2002 is 32.4%
25. In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination?
a) 30000
b) 35000
c) 37000
d) 39000
Discussion
Explanation:
$$\eqalign{ & {\text{Let the total number of applicants be x}}. \cr & {\text{Number of eligible candidates}} \cr & = {\text{ }}95\% {\text{ }}of{\text{ }}x \cr & {\text{Eligible candidates of other categories}}, \cr & = 15\% \,of\,\left( {95\% {\text{ }}of{\text{ }}x} \right) \cr & = {\frac{{15}}{{100}}} \times {\frac{{95}}{{100}}} \times x \cr & = \frac{{57}}{{400}}x \cr & or,\left( {\frac{{57}}{{400}}} \right)x \cr & x = \frac{{ {4275 \times 400} }}{{57}} \cr & \,\,\,\,\,\, = 30000 \cr} $$
26. In a class, the no. of boys is more than the no. of girls by 12% of the total strength. The ratio of boys and girls is:
a) 15 : 11
b) 11 : 14
c) 14 : 11
d) 8 : 11
Discussion
Explanation: Let the no. of total student in the class = 100 and number of boy = X
and 12% of the 100 is 12
Number of girl is x - 12
Total number of student is x + (x - 12) = 100
So, x = 56
No of boys = 56
No. of girls = 44
Boys : Girls = 56 : 44 = 14 : 11
27. In an office there were initially N employees. The HR manager first hired P% employees then after a month Q% employees left the office, the value of (P - Q) is:
a) PQ
b) $$\frac{{{\text{PQ}}}}{{100}}$$
c) $$\frac{{\text{P}}}{{\text{Q}}}$$
d) $$\frac{{\text{Q}}}{{\text{P}}}$$
Discussion
Explanation:
$$\eqalign{ & \frac{{\text{P}}}{{100 + {\text{P}}}} = \frac{{\text{Q}}}{{100}} \cr & 100\left( {{\text{P}} - {\text{Q}}} \right) = {\text{PQ}} \cr & \left( {{\text{P}} - {\text{Q}}} \right) = \frac{{{\text{PQ}}}}{{100}} \cr} $$
28. The amount of work in a leather factory is increased by 50%. By what percent is it necessary to increase the number of workers to complete the new amount of work in previously planned time, if the productivity of the new labour is 25% more.
a) 60%
b) 66.66%
c) 40%
d) 33.33%
Discussion
Explanation: Men × Time = Work
100 × 1 = 100 unit work
150 × 1 = 150 unit work
Extra man power = 50
But, new workers are $$\frac{5}{4}$$ time as efficient as existing workers
So, Actual no. of workers = $$\frac{{50}}{{\frac{5}{4}}}$$ = 40 workers
% required = $$\frac{{40 \times 100}}{{100}} = 40\% $$
29. A big cube is formed by rearranging the 160 coloured and 56 non-coloured similar cubes in such a way that the expouser of the coloured cubes to the outside is minimum. The percentage of exposed area that is coloured is:
a) 25.9%
b) 44.44%
c) 35%
d) 32%
Discussion
Explanation: Total number of cubes = 160 + 56 = 216
Side of cube = 6 unit
No. of cubes without exposure = (6 - 2)3 = 64
Thus 64 cubes will be inside of a big cube
Now, rest cubes = 160 - 64 = 96
No. of cubes with one face outside = 6 × (4 × 4) = 96
Required % = $$\frac{{90 \times 100}}{{216}} = 44.44\% $$
30. 78% of 750 + 34% of x = 30% of 2630. Find x.
a) 960
b) 600
c) 800
d) 750
Discussion
Explanation:
$$\eqalign{ & 78\% \,{\text{of}}\,\,750 + 34\% \,{\text{of}}\,x = 30\% \,{\text{of}}\,\,2630 \cr & {\frac{{ {78 \times 750} }}{{100}}} + \frac{{34x}}{{100}} = \left( {30 \times 2630} \right) \times 100 \cr & 78 \times 750 + 34x = 30 \times 2630 \cr & 34x = 78900 - 58500 \cr & x = \frac{{20400}}{{34}} \cr & x = 600 \cr} $$
31. x * 12 = 75% of 336 Find x.
a) 27
b) 25
c) 21
d) 19
Discussion
Explanation:
$$\eqalign{ & 12x = \frac{{ {75 \times 336} }}{{100}} \cr & x = \frac{{ {75 \times 336} }}{{ {100 \times 12} }} \cr & x = 21 \cr} $$
32. A shop sells floor tiles at Rs. 48 per square meter. A contractor employs a machine that polishes the tiles that damages 10% of the total number of tiles which cannot be used any more. Calculate the amount that needs to be paid by contractor to tile shop owner, if the hall is of a square shape and has a perimeter of 400 meters?
a) Rs. 4,00,000
b) Rs. 5,00,000
c) Rs. 5,28,000
d) Rs. 3,65,000
Discussion
Explanation: Let the side of the square shaped hall be X meter
Perimeter = 4X
4X = 400
X = 100m
Area of the hall = 100 × 100 = 10000 sq. meter.
The cost on total tiles = 10000 × 48 = Rs. 480000
But, 10% damage has occurred on tiles which will also be included in cost i.e
Total cost = 480000 + 10% of 480000 = 480000 + 48000
Total cost = Rs. 5,28,000
33. 125% of 860 + 75% of 480 = ?
a) 1415
b) 1385
c) 1435
d) None of these
Discussion
Explanation:
$$\eqalign{ & { {\frac{{ {125 \times 860} }}{{100}}} + {\frac{{75 \times 480}}{{100}}} } \cr & = 1075 + 360 \cr & = 1435 \cr} $$
34. A person subscribing to sky cable for a year pack Rs. 1785. If the monthly subscription is Rs. 175, how much discount does a yearly subscriber get?
a) 11%
b) 13%
c) 15%
d) 18%
Discussion
Explanation: Yearly subscription rate = Rs. 1785
Charge for 12 month as rate Rs. 175 per month
= 12 × 175 = Rs. 2100
Discount = 2100 - 1785 = Rs. 315
% discount = $$\frac{{315 \times 100}}{{2100}}$$ = 15%
35. In a metro train there are 600 passengers out of which 34% are females. Fare of each male is Rs. 20 and each female's fare is 25% less than each male. What is the total revenue generated by all the passengers together?
a) Rs. 10880
b) Rs. 10980
c) Rs. 10740
d) Rs. 10680
Discussion
Explanation: Total Passengers = 600
No. of females = $$\frac{{600 \times 34}}{{100}}$$ = 204
No. of male passengers
= 600 - 204 = 396
Fare of each male = Rs. 20
Fare of female, 15% less,
= $$\frac{{20 \times 75}}{{100}}$$ = Rs. 15 each
Total revenue generated by male
= 396 × 20
= Rs. 7920
Total revenue generated by female
= 204 × 15
= 3060
Total Revenue
= 7920 + 3060
= Rs. 10980
36. In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State ?
a) 7600
b) 8000
c) 8400
d) 8800
Discussion
Explanation: Let the number of candidates appearing from each state be X.
7% of X - 6% of X = 80
1% of X = 80
X = 80 × 100
X = 8000
37. Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get ?
a) 45 %
b) 57 %
c) 60 %
d) 65 %
Discussion
Explanation:
$$\eqalign{ & {\text{Total number all three got together is}} \cr & = {1136 + 7636 + 11628} \cr & = 20400 \cr & \% {\text{ of vote the winning candidate got is}} \cr & = {\frac{{11628}}{{20400}}} \times 100 \cr & = 57\% \cr} $$
38. Fresh grapes contain 80% while dry grapes contain 10% water. If the weight of dry grapes is 250 kg, what was its total weight when it was fresh?
a) 1000 kg
b) 1125 kg
c) 1225 kg
d) 1100 kg
Discussion
Explanation: Quantity of water in 250 kg dry grapes,
$$ = \frac{{10}}{{100}} \times 250 = 25\,{\text{kg}}$$
Pulp of grapes = 225 kg
We get 20 kg pulp in 100 kg fresh grapes.
To get 225 kg pulp, we need fresh grapes,
$${\text{ = }}\frac{{100 \times 225}}{{20}} = 1125\,{\text{kg}}$$
39. A population of variety of tiny bush in an experiment field increased by 10% in the first year, increased by 8% in the second year but decreased by 10% in third year. If the present number of bushes in the experiment field is 26730, then the number of variety of bushes in beginning was:
a) 35000
b) 27000
c) 25000
d) 36000
Discussion
Explanation: Let the number of bushes originally be 100
Number of bushes after one year
100 ==10% (↑) ==> 110
After second year it becomes
110 ==8%(↑) ==> 118.8
After third year,
118.8 ==8%(↓)==> 109.3
Now,
109.3 = 26730
1 = $$\frac{{26730}}{{109.3}}$$
So, 100 = $$\frac{{26730}}{{109.3}} \times 100$$ = 25000
Number of bushes originally was 25000
40. If a% of x is equal to b% of y, then of c% of y is what % of x ?
a) c %
b) $$\frac{{{\text{ac}}}}{{\text{b}}}$$ %
c) $$\frac{{{\text{bc}}}}{{\text{a}}}$$ %
d) abc %
Discussion
Explanation:
$$\eqalign{ & \frac{{ {ax} }}{{100}} = \frac{{ {by} }}{{100}} \cr & ax = by \cr & y = \frac{{ {ax} }}{b} \cr & c\% \,{\text{of}}\,y = \frac{{ {cy} }}{{100}} \cr & \frac{{ {cy} }}{{100}} = \frac{{ {cax} }}{{100b}} \cr & c\% \,{\text{of}}\,y = \frac{{ca}}{b}\% \,{\text{of}}\,x \cr} $$
41. A litre of water evaporates from 6L of sea water containing 4% salt. Find the percentage of salt in the remaining solution.
a) $$5\frac{1}{2}\% $$
b) $$3\frac{1}{2}\% $$
c) 3%
d) $$4\frac{4}{5}\% $$
Discussion
Explanation:
$$\eqalign{ & {\text{Quantity of salt in 6L of sea water,}} \cr & = \frac{{ {6 \times 4} }}{{100}} = 0.24 \cr & {\text{Percentage of salt in 5L of sea water,}} \cr & = \frac{{ {0.24 \times 100} }}{5} = 4\frac{4}{5}\% \cr} $$
42. Two discount of 8% and 12% are equal to a single discount of:
a) 20%
b) 19.04%
c) 22.96%
d) 22%
Discussion
Explanation: After first discount,
100 ---- 8%↓ ----> 92
After second discount,
92 ---- 12%↓ ----> 80.96
Single discount = 100 - 80.96 = 19.04%
43. In a library 60% of the books are in Hindi, 60% of the remaining books are in English rest of the books are in Urdu. If there are 3600 books in English, then total no. of books in Urdu are:
a) 2400
b) 2500
c) 3000
d) 3200
Discussion
Explanation: Let there are X books in the library.
Number of Hindi books = 60% of X = $$\frac{{60{\text{X}}}}{{100}}$$ = 0.6X
Remaining Books = X - 0.6X = 0.4X
Number English books = 40% of reaming books = 60% of 0.4X = 0.24X.
Urdu Books = X-0.6X -0.24X = 0.16X
0.24X = 3600
X $$ = \frac{{3600}}{{0.24}} = 15000$$
Urdu Books = 0.16X = 0.16 × 15000 = 2400
44. In Sabarmati Express, there as many wagons as there are the no. of seats in each wagon and not more than one passenger can have the same berth (seat). If the middlemost compartment carrying 25 passengers is filled with 71.428% of its capacity, then find the maximum no. of passengers in the train that can be accommodated if it has minimum 20% seats always vacant.
a) 500 seats
b) 786 seats
c) 980 seats
d) 1060 seats
Discussion
Explanation: Total number of passenger in each compartment = $$\frac{{ {25 \times 7} }}{5}$$ = $$35$$
Total berth = 352 = 1225
Maximum available capacity
$$\eqalign{ & = \frac{{ {1225 \times 80} }}{{100}} \cr & = 980\,{\text{seats}} \cr} $$
45. The population of a village is 5000 and it increases at the rate of 2% every year. After 2 years, the population will be:
a) 5116
b) 5202
c) 5200
d) 5204
Discussion
Explanation:
$$\eqalign{ & {\text{Population after two years}}, \cr & = 5000 \times {\left[ {1 + {\frac{2}{{100}}} } \right]^2} \cr & = 5202 \cr} $$
46. The schedule working hour of a labour in a week if 48 hours and he gets Rs. 480 for that. Over time rate is 25% more than the the basic salary rate. In a week a labour gets Rs. 605, how many hours altogether he works in that week.
a) 49 hours
b) 52 hours
c) 55 hours
d) 58 hours
Discussion
Explanation: Schedule working hours in week = 48
Total pay in a week for schedule working hours = Rs. 480
Pay per hour for schedule working hours = $$\frac{{480}}{{48}}$$ = Rs. 10
Pay per hour for over time = 10 + 25% of 10 = Rs. 12.5
Total pay in that particular week = Rs. 605
Extra pay = 605 - 480 = 125
So, total over time = $$\frac{{125}}{{12.5}}$$ = 10 hours
Total work hour altogether in that week = 48 + 10 = 58 hours
47. In an election 4% of the votes caste become invalid. Winner gets 55% of casted votes and wins the election by a margin of 4800 votes. Find the total number of votes casted.
a) 45000
b) 48000
c) 50000
d) 52000
Discussion
Explanation: Winner gets 55% of votes.
As 4% votes were declared invalid so 96% would be the valid votes
So, Winner gets 55% of 96% valid votes
Winner gets % valid votes = $$\frac{{55 \times 96}}{{100}}$$ = 52.8% votes
Loser gets = 96 - 52.8 = 43.2% votes
Difference = 9.6%
9.6% = 4800
1% = $$\frac{{4800}}{{9.66}}$$
100% Votes = $$\frac{{4200 \times 100}}{{9.66}}$$ = 50000
Total Voters = 50000
48. A reduction of 10% in the price of cloth enables a man to buy 6 meters of cloth more for Rs. 2160. Find the reduced price and also the original price of cloth per meter.
a) Rs. 36, Rs. 40
b) Rs. 40, Rs. 36
c) Rs. 36, Rs. 44
d) Rs. 44, Rs. 36
Discussion
Explanation: Money spent originally = Rs. 2160
Less money to be spent for now for the same length of cloth,
= 10% of 2160 = Rs. 216
It means Rs. 216 enables a man to buy 6 meters of cloth
Reduced price = $$\frac{{216}}{6}$$ = Rs. 36 per meter
Original price = $$\frac{{100 \times 36}}{{90}}$$ = Rs. 40 per meter
49. A gardener increased the rectangular garden by increasing its length by 40% and decreasing its width by 20%. The area of the new garden:
a) Has increased by 20%
b) Has increased by 12%
c) Has increased by 8%
d) Is exactly the same as the old area
Discussion
Explanation: Let original area of the garden was 100 square unit.
Increase or decrease in area can be easily determined by this graphic:
100 == 40% up length ==> 140 == 20% down width ==> 112 (Final Area)
There is 12% increase in area of the garden.
50. If A exceeds B by 40%, B is less than C by 20%, then A : C is
a) 28 : 25
b) 26 : 25
c) 3 : 2
d) 3 : 1
Discussion
Explanation: Let B = 100
A = 100 + 40% of 100 = 140
Let C = X
X - 20% of X = 100
0.8X = 100
X = $$\frac{{100}}{{0.8}}$$ = 125
A : C = $$\frac{{140}}{{125}}$$ = 28 : 25
51. A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
a) 45%
b) $$45\frac{5}{{11}}\% $$
c) $$54\frac{6}{{11}}\% $$
d) 55%
Discussion
Explanation: Number of runs made by running
= 110 - (3 x 4 + 8 x 6)
= 110 - (60)
= 50
Required percentage
$$\eqalign{ & = \left( {\frac{{50}}{{110}} \times 100} \right)\% \cr & = 45\frac{5}{{11}}\% \cr} $$
52. Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:
a) 39, 30
b) 41, 32
c) 42, 33
d) 43, 34
Discussion
Explanain : Let their marks be (x + 9) and x
$$\eqalign{ & x + 9 = \frac{{56}}{{100}}\left( {x + 9 + x} \right) \cr & 25\left( {x + 9} \right) = 14\left( {2x + 9} \right) \cr & 3x = 99 \cr & x = 33 \cr} $$
So, their marks are 42 and 33
53. A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
a) 588 apples
b) 600 apples
c) 672 apples
d) 700 apples
Discussion
Explanation: Suppose originally he had x apples
$$\eqalign{ & \left( {100 - 40} \right)\% \,{\text{of}}\,x = 420 \cr & \frac{{60}}{{100}} \times x = 420 \cr & x = {\frac{{420 \times 100}}{{60}}} = 700 \cr} $$
54. What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
a) 1%
b) 14%
c) 20%
d) 21%
Discussion
Explanation: The numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1.
Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number = 14
$$ = \left( {\frac{{14}}{{70}} \times 100} \right)\% = 20\% $$
55. If A = x% of y and B = y% of x, then which of the following is true?
a) A is smaller than B
b) A is greater than B
c) Relationship between A and B cannot be determined
d) None of these
Discussion
Explanation:
$$\eqalign{ & x\% \,{\text{of}}\,y = {\frac{x}{{100}} \times y} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\frac{y}{{100}} \times x} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = y\% \,{\text{of}}\,x \cr & So, A = B \cr} $$
56. Due to fall of 10% in the rate of sugar, 500 gm more sugar can be purchased for Rs. 140. Find the original rate?
a) Rs. 31.11
b) Rs. 29.22
c) Rs. 33.11
d) Rs. 32.22
Discussion
Explanation: Money spent originally = Rs. 140
Less Money to be spent now
= 10% of 140
= Rs. 14
Rs. 14 now yield 500 gm sugar
So, Present rate of sugar = Rs. 28 per kg.
If the present value is Rs. 90, the original value = Rs. 100
If the present value is Rs. 28 the original value
$$ = {\text{Rs}}{\text{. }}\frac{{100}}{{90}} \times 28 = {\text{Rs}}{\text{. }}31.11$$
57. Two numbers are respectively 20% and 50% of a third number. What percent is the first number of second?
a) 10%
b) 20%
c) 30%
d) 40%
Discussion
Explanation:
$$\eqalign{ & {\text{Let third number is x}}. \cr & {\text{Then}}\,{\text{first}}\,{\text{no}}{\text{.}} \cr & 20\% \,{\text{of}}\,x = \frac{{20x}}{{100}} \cr & {\text{Second}}\,{\text{number}} \cr & = 50\% \,{\text{of}}\,x = \frac{{50x}}{{100}} \cr & {\text{Percent of first no of second no,}} \cr & = {\frac{{ {\frac{{20x}}{{100}}} }}{{ {\frac{{50x}}{{100}}} }}} \times 100 \cr & = \frac{{ {2 \times 100} }}{{20}} \cr & = 40\% \cr} $$
58. An empty fuel tank of a car was filled with A type petrol. When the tank was half-empty, it was filled with B type petrol. Again when the tank was half-empty, it was filled with A type petrol. When the tank was half-empty again, it was filled with B type petrol. What is the percentage of A type petrol at present in the tank?
a) 33.5%
b) 37.5%
c) 40%
d) 50%
Discussion
Explanation: Let the capacity of the tank be 100 litres
Initially, A type petrol = 100 litres
After first operation:
A type petrol = $$\frac{{100}}{2}$$ = 50 litres
B type petrol = 50 litres
After second operation:
A type petrol = $$\frac{{50}}{2}$$ + 50 = 75 litres
B type petrol = $$\frac{{50}}{2}$$ = 25 litres
After third operation:
A type petrol = $$\frac{{75}}{2}$$ = 37.5 litres
B type petrol = $$\frac{{25}}{2}$$ + 50 = 62.5 litres
Required percentage = 37.5%
59. For an examination it is required to get 36% of maximum marks to pass. A student got 113 marks and failed by 85 marks. The maximum marks for the examination are:
a) 500
b) 550
c) 565
d) 620
Discussion
Explanation: 36% marks = 113 + 85
36% marks = 198
So, 1% marks = $$\frac{{198}}{{36}}$$ = 5.5
100% marks = 5.5 × 100 = 550
60. 1% of 1% of 25% 1000 is
a) 0.025
b) 0.0025
c) 0.25
d) 0.000025
Discussion
Explanation:
$$\eqalign{ & 1\% \,{\text{of}}\,1\% \,{\text{of}}\,25\% \,1000 \cr & = 1\% \,{\text{of}}\,1\% \,{\text{of}}\,\, {\frac{{ {25 \times 1000} }}{{100}}} \cr & = 1\% \,{\text{of}}\,1\% \,{\text{of}}\,250 \cr & = 1\% \,{\text{of}}\,\, {\frac{{ {1 \times 200} }}{{100}}} \cr & = 1\% \,{\text{of}}\,\,2.5 \cr & = \frac{{2.5}}{{100}} \cr & = 0.025 \cr} $$
61. Heinz produces tomato puree by boiling tomato juice. Tomato puree has 20% water whereas tomato juice has 90% water.How many litres of tomato puree will be obtained from 20 litres of tomato juice ?
a) 2 litres
b) 3 litres
c) 2.5 litres
d) 5 litres
Discussion
Explanation: 20 litres juice contain 10% Tomato, i.e.
20L juice = $$\frac{{20 \times 10}}{{100}}$$ = 2L Tomato
Tomato puree contains 80% of water and 20% tomato.
This 80% tomato = 2L (which is contained by 100 puree)
Now this 2 L Consist 80% in puree
Total puree will be $$\frac{2}{{0.8}} = 2.5{\text{L}}$$
62. What is the percentage change in the result when we add 50 to a certain number x, instead of subtracting 50 from the same number x?
a) 50 %
b) 75 %
c) 100 %
d) Can't be determined
Discussion
Explanain : If we take different values of x then,
Let x = 150, then error%
$$\eqalign{ & = \frac{{ {\frac{{ {200 - 100} }}{{100}}} }}{{100}} \cr & = 100\% \cr} $$
Again if x = 100, then error%
$$\eqalign{ & = \frac{{ {\left( {150 - 50} \right) \times 100} }}{{100}} \cr & = 200\% \cr} $$
If we take different value of x, then we get different answer so we can't determine it.
63. In a school, there are 100 students. 60% of the students are boys, 40% of whom play hockey and the girls don't play hockey, 75% of girls play badminton. There are only two games to be played. The number of student who don't play any game is:
a) 10 %
b) 20 %
c) 36 %
d) Can't be determined
Discussion
Explanation: Total student = 100
Boys = 60
Girls = 40
Boys who plays hockey = 40% = 24
There is no information about boys who play badminton.
Girls who plays Badminton = 75% = 30
No girls plays hockey.
Since, we do not have information that whether the rest of the boys are playing badminton or not. So, we cannot determine the total no. of student who don't play any game.
64. A book consist of 30 pages, 25 line on each page and 35 characters on each line. If this content is written in another note book consisting 30 lines and 28 characters per line then the required no. of pages will how much percent greater than previous pages?
a) 4.16%
b) 5%
c) 6.66%
d) 7%
Discussion
Explanation:
$$\eqalign{ & {\text{Let the required number of pages be }}x. \cr & 30 \times 25 \times 35 = x \times 30 \times 28 \cr & x = 31.25 \approx 32 \cr & \% \,{\text{increase}}\,{\text{in}}\,{\text{number}}\,{\text{of}}\,{\text{pages}}, \cr & = {\frac{2}{{30}}} \times 100 \cr & = 6.66\% \cr} $$
65. A fraction in reduced form is such that when it is squared and then its numerator is increased by 25% and the denominator is reduced to 80% it results in $$\frac{5}{8}$$ of original fraction. The product of the numerator and denominator is
a) 6
b) 12
c) 10
d) 7
Discussion
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{fraction}}\,{\text{be}}\,\frac{{100x}}{{100y}} \cr & {\text{According}}\,{\text{to}}\,{\text{the}}\,{\text{question}}, \cr & {\left( {\frac{{100x}}{{100y}}} \right)^2} = \frac{{125{x^2}}}{{80{y^2}}} = \frac{{25{x^2}}}{{16{y^2}}} \cr & \frac{{25{x^2}}}{{16{y^2}}} = \frac{5}{8}\left( {\frac{{100x}}{{100y}}} \right) \cr & {\frac{{100x}}{{100y}}} = \frac{2}{5} \cr & {\text{product of numerator and denominator}} \cr & = 2 \times 5 = 10 \cr} $$
66. Mr. X salary increased by 20%. On the increase, the tax rate is 10% higher. The percentage increase in tax liability is:
a) 20 %
b) 22 %
c) 23 %
d) 24 %
Discussion
Explanation: Let his original salary be Rs. 100
Salary after increment = Rs. 120
Let the tax on original salary be 20% and now tax on increased salary (Rs. 20) will be 22% i.e. Rs. 4.40
Increase in tax liability $$ = \frac{{4.40}}{{20}} \times 100 = 22\% $$
67. The total emoluments of A and B are equal. However, A gets 65% of his basic salary as allowances and B gets 80% of his basic salary as allowances. What is the ratio of the basic salaries of A and B?
a) 16 : 13
b) 5 : 7
c) 12 : 11
d) 7 : 9
Discussion
Explanation: Let the basic salaries of A and B be x and y respectively.
$$\eqalign{ & x + 65\% \,\,{\text{of }}x = y + 80\% \,\,{\text{of }}y \cr & x + \frac{{ {65x} }}{{100}} = y + \frac{{ {80y} }}{{100}} \cr & \frac{x}{y} = \frac{{180}}{{165}} \cr & x:y = 12:11 \cr} $$
68. Distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A traveled uniformly with average speed of 4 km/hr. The other man traveled with varying speed as follows: In the first hour his speed 2 km/hr, in the second hour it was 2.5 km/hr, in the third hour it was 3 km/hr, and so on. When/where will they meet each other?
a) 7 hours after starting
b) 10 hours after starting
c) 35 km from AMid-way between A and B
d) 50%
Discussion
Explanation: They covered the distance in this way together in different hours
6 + 6.5 + 7 + 7.5 + 8 + 8.5 + 9 + 9.5 + 10 = 72 Means, they'll meet at the 9th hr.
So, In that time A will cover = 4 × 9 = 36km
They will meet in Midway
69. In company there are 75% skilled workers and reaming are unskilled. 80% of skilled workers and 20% of unskilled workers are permanent. If number of temporary workers is 126, then what is the number of total workers ?
a) 480
b) 510
c) 360
d) 377
Discussion
Explanation:
$$\eqalign{ & {\text{Let the number of total workers}} = x \cr & {\text{Number of skilled workers}} \cr & = 75\% \,of\,x = \frac{{75x}}{{100}} = \frac{{3x}}{4} \cr & {\text{No}}{\text{. of unskilled workers}} \cr & = 25\% \,of\,x = \frac{{25x}}{{100}} = \frac{x}{4} \cr & {\text{No}}{\text{. of permanent workers}}, \cr & = {\frac{{80}}{{100}}} \times {\frac{{3x}}{4}} + {\frac{{20}}{{100}}} \times {\frac{x}{4}} \cr & = {\frac{{3x}}{5}} + {\frac{x}{{20}}} \cr & = \frac{{13x}}{{20}} \cr & {\text{No}}{\text{.}}\,{\text{of}}\,{\text{temporary}}\,{\text{workers}} = \cr & x - {\frac{{13x}}{{20}}} = \frac{{7x}}{{20}} \cr & \frac{{7x}}{{20}} = 126 \cr & x = 360 \cr} $$
70. Population of a district is 2,96,000 out of which 1,66,000 are male. 50% of the population is literate. If 70% males are literate, then the number of woman who are literate, is
a) 32,200
b) 31,800
c) 66,400
d) 48,000
Discussion
Explanation: No. of population who are literate = 50% of 296000 = 148000
No. of male = 166000
No. of female = 296000 - 166000 = 130000
No. of literate male = 70% of 166000 = 116200
No. of literate women
= 148000 - 116200
= 31800
71. The rate of increase of the price of sugar is observed to be two percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994 is Rs. 20 per kg. The inflation rates of the years 1994 and 1995 are expected to be 8% each. The expected price of sugar on January 1, 1996 would be
a) Rs. 23.60
b) Rs. 24
c) Rs. 24.20
d) Rs. 24.60
Discussion
Explanation: Increase in the price of sugar = (8 + 2) = 10%
Price of sugar on Jan. 1, 1996
$$\eqalign{ & = \frac{{20 \times 110 \times 110}}{{100 \times 100}} \cr & = {\text{Rs}}{\text{.}}\,24.20 \cr} $$
72. In an examination, questions were asked in five sections. Out of the total students, 5% candidates cleared the cut-off in all the sections and 5% cleared none. Of the rest, 25% cleared only one section and 20% cleared four sections. If 24.5% of the entire candidates cleared two sections and 300 candidates cleared three sections. Find out how many candidates appeared at the examination?
a) 1000
b) 1200
c) 1500
d) 2000
Discussion
Explanain : Passed in none = 5%
Passed in all = 5%
Passed in four = 20% of 90% = 18%
Passed in one = 25% of 90% = 22.5%
Passed in two = 24.5%
Passed in three = (100 - 5 - 5 - 22.5 - 24.5 - 18) = 25%
But given 300 students passed in three
Hence, 25% = 300
So, 100% = 1200
1200 students must have appeared
73. A clock is set right at 12 noon on Monday. It losses $$\frac{1}{2}$$ % on the correct time in the first week but gains $$\frac{1}{4}$$ % on the true time during the second week. The time shown on Monday after two weeks will be
a) 12 : 25 : 12
b) 11 : 34 : 48
c) 12 : 50 : 24
d) 12 : 24 : 16
Discussion
Explanation: Time lost over two weeks = 25% a week time(given that $$\frac{1}{2}$$ % clock loses in first week and in the second week it gains $$\frac{1}{4}$$ % on true time)
A week = 168 hours
clock lost = 0.42 hours = 25.2 minutes or 25 minute 12 seconds
correct time = 11 : 34 : 48
74. If a 36 inches long strip cloth shrinks to 33 inches after being washed, how many inches long will the same strip remain after washing if it were 48 inches long?
a) 47 inches
b) 44 inches
c) 45 inches
d) 46 inches
Discussion
Explanation:
$$\eqalign{ & {\text{Shrinking of cloth}}, \cr & = {\frac{{ {36 - 33} }}{{36}}} \times 100 \cr & = \frac{{100}}{{12}}\% \cr & {\text{Second time the strip shrinks,}} \cr & = \frac{{ {48 \times 100} }}{{1200}} \cr & = 4\,\text{inches} \cr & {\text{The}}\,{\text{cloth}}\,{\text{remains}} \cr & = 48 - 4 \cr & = 44 \cr} $$
75. (X% of Y) + (Y% of X) is equal to:
a) X% of Y
b) 20% of XY
c) 2% of XY
d) 2% of 100 XY
Discussion
Explanation:
$$\eqalign{ & {\frac{{XY}}{{100}}} + {\frac{{YX}}{{100}}} \cr & = \frac{{2XY}}{{100}} \cr & = 2\% \,of\,XY \cr} $$
76. The actual area of a rectangle is 60 cm2, but while measuring its length a student decreases it by 20% and the breadth increases by 25%. The percentage error in area, calculated by the student is :
a) 5 %
b) 15 %
c) 20 %
d) No change
Discussion
Explanation: 100 === 25% ↑===> 125 ===> 20% ↓===> 100
So, there is no change in the area of rectangle
77. The cost of packaging of the mangoes is 40% the cost of fresh mangoes themselves. The cost of mangoes increased by 30% but the cost of packaging decreased by 50%, then the percentage change of the cost of packed mangoes, if the cost of packed mangoes is equal to the sum of the cost of fresh mangoes and cost of packaging :
a) 14.17%
b) 7.14%
c) 8.87%
d) 6.66%
Discussion
Explanation: Cost of fresh mangoes + Cost of packaging = Total cost
Let initial Cost of fresh, mangoes = 100
packaging cost = 40
Initial total cost = 100 + 40 = 140
After increasing in cost of fresh mangoes 30%,
Cost of fresh mangoes = 130
And cost of packing go down by 50 % so,
Cost of packing = 20
Now Total cost = 130 + 20 = 150
Increased cost = 150 - 140 = 10
% increased = $$ = \frac{{10 \times 100}}{{140}} = 7.14\% $$
78. 220% of a number X is 44. What is 44% of X.
a) 8.8
b) 8.9
c) 6.6
d) 7.7
Discussion
Explanation: 220% of X = 44
X = 20
Thus, 44% of 20
$$ = \frac{{44 \times 20}}{{100}} = 8.8$$
79. The shopkeeper increased the price of a product by 25% so that customer finds difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product ?
a) 55 more
b) 10% more
c) 12.5% less
d) 17.5% less
Discussion
Explanation: Let initially the quantity and rate be 100 each
Quantity × rate = Expenditure
100 × 100 = 10000
Now, Increase in price is 25% and new quantity is 70% of original
Quantity × rate = Expenditure
70 × 125 = 8750
Decreased expenditure,
= 10000 - 8750 = 1250
% decrease $$ = \frac{{1250 \times 100}}{{10000}} = 12.5\% $$
80. A customer asks for the production of x number of goods. The company produces y number of goods daily. Out of which z% are units for sale. The order will be completed in :
a) $$ {\frac{x}{{100y \times \left( {1 - z} \right)}}} \,{\text{days}}$$
b) $$ {\frac{{100yz}}{x}} \,{\text{days}}$$
c) $$ {\frac{{100x}}{{\left( {100 - z} \right)y}}} \,{\text{days}}$$
d) $$\frac{{100}}{{y \times \left( {z - 1} \right)}}\,{\text{days}}$$
Discussion
Explanation:
$$\eqalign{ & {\text{Daily}}\,{\text{supply}} \cr & = \left( {100 - z} \right)\% \,{\text{of}}\,y \cr & = \frac{{ {\left( {100 - z} \right)y} }}{{100}} \cr & {\text{Required}}\,{\text{number}}\,{\text{of}}\,{\text{days}} \cr & = {\frac{{ {100x} }}{{\left( {100 - z} \right)y}}} \cr} $$
81. In the Science City, Kolkata the rate of the ticket is increased by 50% to increased the revenue but simultaneously 20% of the visitor decreased. What is percentage change in the revenue. if it is known that the Science city collects one revenue only from the visitors and it has no other financial supports:
a) +20%
b) -25%
c) +30%
d) -30%
Discussion
Explanation: Let the initial revenue be 100
100 === 50% ↑ (Ticket up) ===> 150 === 20% ↓ (Visitors down) ===> 120
There is 20% increase in the revenue
82. Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
a) 57%
b) 60%
c) 65%
d) 90%
Discussion
Explanain : Total number of votes polled
= (1136 + 7636 + 11628)
= 20400
Required percentage
= $$\left( {\frac{{11628}}{{20400}} \times 100} \right)\% $$
= $$57\% $$
83. An alloy contains the copper and aluminum in the ratio of 7 : 4 While making the weapons from this alloy, 12% of the alloy got destroyed. If there is 12 kg of aluminum in the weapon, then weight of the alloy required is :
a) 14.4 kg
b) 37.5 kg
c) 40 kg
d) 48 kg
Discussion
Explanation: Copper : Aluminum = 7 : 4
Let Copper and Aluminum in the weapon be 7x and 4x respectively
Given, Aluminum in weapon = 12 kg
So, 4x = 12
x = 3
Copper = 7x = 7 × 3 = 21 Kg.
Total alloy in the weapon = 12 + 21 = 33 kg
But 12% alloy get destroyed in making the weapon, i.e. 88% alloy is used in the weapon,
88 % alloy = 33 kg
100 % alloy = 37.5 kg
84. 80% of a smaller number is 4 less than 40% of a larger number. The larger number is 85 greater than the smaller one. The sum of these two number is
a) 325
b) 425
c) 235
d) 500
Discussion
Explanation: Let the smaller number be x and larger number be y
According to the question,
80% of x + 4 = 40% of y
4y - 8x = 40
y - 2x = 10 ----- (1)
y - x = 85 ----- (2)
By using (1) and (2),
x = 75
y = 160
x + y = 235
85. A number x is mistakenly divided by 10 instead of being multiplied by 10. what is the percentage error in the result?
a) -99%
b) -100%
c) +99%
d) +100%
Discussion
Explanation: Actual result = 10x
By mistake it has been divided by 10 = $$\frac{x}{{10}}$$
%Change = $$ {\frac{{10x - \left( {\frac{{10}}{x}} \right)}}{{10x}}} $$ × 100 = 99 = -99%
Since, actual value is greater than the wrong value.
86. Out of the total production of iron from hematite, an ore of Iron, 20% of the ore gets wasted, and out of the remaining iron, only 25% is pure iron. If the pure iron obtained in a year from a mine of hematite was 80,000 kg, then the quantity of hematite mined from that mine in the year is
a) 5,00,000 kg
b) 4,00,000 kg
c) 4,50,000 kg
d) None of these
Discussion
Explanation: Let 100 kg of hematite be obtained then 20% of it get wasted that means 80 kg of ore remains.
Pure iron = 25% of remaining ore = $$\frac{{80 \times 25}}{{100}} = 20\,{\text{kg}}$$
20 kg pure Iron is obtained from 100 of hematite
1 kg pure Iron is obtained from = $$\frac{{100}}{{20}}$$ hematite
80000 kg pure Iron is obtained from =$$\,\frac{{100}}{{20}} \times 80000 = \,$$ $$400000\,{\text{kg}}$$ hematite.
87. A man buys a truck for Rs. 2,50,000. The annual repair cost comes to 2% of the price of purchase. Besides, he has to pay an annual tax of Rs. 2000. At what monthly rent must he rent out the truck to get a return of 15% on his net invests of the first year?
a) Rs. 3359
b) Rs. 2500
c) Rs. 4000
d) Rs. 3212.5
Discussion
Explanation: The total cost for the year
= 250000 + 2% of 2500000 + 2000
= Rs. 257000
For getting return of 15% he must earn
= $$\frac{{257000 \times 15}}{{100}}$$
= Rs. 38550 per year
Monthly Rent = $$\frac{{38550}}{{12}}$$
= Rs. 3212.5
88. Ram spends 30% of his salary on house rent, 30% of the rest he spends on his children's education and 24% of the total salary he spends on clothes. After his expenditure, he is left with Rs. 2500. What is Ram's salary?
a) Rs. 11,494.25
b) Rs. 20,000
c) Rs. 10,000
d) Rs. 15,000
Discussion
Explanation: Let Ram's salary be x
He spends on rent = 30% of x = $$\frac{{30{\text{x}}}}{{100}}$$
He spends on education = 30% from rest of the salary = $$\frac{{30 \times 70{\text{x}}}}{{100 \times 100}} = \frac{{21{\text{x}}}}{{100}}$$
He Spends on clothes = 24% of total salary = $$\frac{{24{\text{x}}}}{{100}}$$
Saving = 2500
Salary of ram = x
$$\eqalign{ & \frac{{30{\text{x}}}}{{100}} + \frac{{21{\text{x}}}}{{100}} + \frac{{24{\text{x}}}}{{100}} + 2500 = {\text{x}} \cr & \frac{{75x}}{{100}} = {\text{x}} - 2500 \cr & 75{\text{x}} = 100{\text{x}} - 250000 \cr & 100{\text{x}} - 75{\text{x}} = 250000 \cr & {\text{x}} = \frac{{250000}}{{25}} \cr & {\text{x}} = 10000 \cr & {\text{Ram's}}\,{\text{salary = Rs}}{\text{.}}\,10000 \cr} $$
89. A report consists of 20 sheets each of 55 lines and each such line consist of 65 characters. This report is reduced onto sheets each of 65 lines such that each line consists of 70 characters. The percentage reduction in number of sheets is closer to
a) 20%
b) 5% more
c) 30% less
d) 35% less
Discussion
Explanation: Let x be the page required when report is retyped
Now, we can use work equivalence method
20 × 55 × 65 = 70 × 65 × x
x = $$\frac{{20 \times 55 \times 65}}{{70 \times 65}}$$
x = 15.70 = 16 pages.
% reduction in pages = $$\left( {20 - 16} \right) \times \frac{{100}}{{20}}$$ $$\, = \,$$ $$20\% $$
90. The price of Maruti car rises by 30 percent while the sales of the car come down by 20%. What is the percentage change in the total revenue?
a) - 4%
b) - 2%
c) + 4%
d) + 2%
Discussion
Explanation: 100 == 30%↑(price effect) ==> 130 == 20%↓(sales effects) ==> 104
Hence, 4% rises
91. In an institute, 60% of the students are boys and the rest are girls. Further 15% of the boys and 7.5% of the girls are getting a fee waiver. If the number of those getting a fee waiver is 90, find the total number of students getting 50% concessions if it is given that 50% of those not getting a fee waiver are eligible to get half fee concession?
a) 360
b) 280
c) 320
d) 330
Discussion
Explanation: Let us assume there are 100 students in the institute.
Then, number of boys = 60
number of girls = 40
Further, 15% of boys get fee waiver = 9 boys
7.5% of girls get fee waiver = 3 girls
Total = 12 students who gets fee waiver
But, here given 90 students are getting fee waiver. So we compare
12 = 90
So, 1 = $$\frac{{90}}{{12}}$$ = 7.5
Now number of students who are not getting fee waiver = 51 boys and 37 girls
50% concession = 25.5 boys and 18.5 girls (i.e. total 44)
Required students = 44 × 7.5 = 330
92. After three successive equal percentage rise in the salary the sum of 100 rupees turned into 140 rupees and 49 paise. Find the percentage rise in the salary.
a) 12%
b) 22%
c) 66%
d) 82%
Discussion
Explanain : Solve it through options
100 == 12% up ==> 112 == 12% up ==> 125.44 == 12% Up ==> 140.49
So, answer is 12%
93. A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6:7:8:9:10. In all papers together, the candidate obtained 60% of the total marks then, the number of papers in which he got more than 50% marks is
a) 1
b) 3
c) 4
d) 5
Discussion
Explanation: Let the marks obtained in five subjects be 6x, 7x, 8x, 9x and 10x.
Total marks obtained = 40x
Max. Marks of the five subjects = $$\frac{{40{\text{x}}}}{{0.6}}$$ [40x is 60% of total marks]
Max. Marks in each subject = $$\frac{{40{\text{x}}}}{{0.6 \times 5}}$$ = 13.33x
Hence, % of each subject = $$\frac{{6{\text{x}} \times 100}}{{13.33}}$$ = 45.01%
$$\frac{{7{\text{x}} \times 100}}{{13.33}}$$ = 52.51
In same way other percentage are 60.01%, 67.52%, 75.01%.
Number of subjects in which he gets more than 50% marks = 4
94. The length, breadth and height of a room are in ratio 3:2:1. If breadth and height are halved while the length is doubled, then the total area of the four walls of the room will
a) remain the same
b) decrease by 13.64%
c) decrease by 15%
d) decrease by 30%
Discussion
Explanation: Let length, breadth and height of the room be 3, 2, 1 unit respectively.
Area of walls = 2(l + b) × h = 2(3 + 2) × 1 = 10 sq. unit.
Now, length, breadth and height of room will become 6, 1 and $$\frac{1}{2}$$ respectively.
Area of walls = $$2\left( {6 + 1} \right) \times \frac{1}{2}$$ = 7 sq. unit.
% decrease in the area of walls = $$\left( {10 - 7} \right) \times \frac{{100}}{{10}}$$ = 30%
95. One bacterium splits into eight bacteria of the next generation. But due to environment, only 50% of one generation can produced the next generation. If the seventh generation number is 4096 million, what is the number in first generation?
a) 1 million
b) 2 million
c) 4 million
d) 8 million
Discussion
Explanation: Let the number of bacteria in the 1st generation be x, then number of bacteria in 2nd, 3rd, 4th . . . . . Generation would be
$$8\left( {\frac{{\text{x}}}{2}} \right),\,8\left( {\frac{{4{\text{x}}}}{2}} \right),\,8\left( {\frac{{16{\text{x}}}}{2}} \right)$$ . . . . And so on.
As x, 4x, 16x, 64x . . . . . it is in GP with common ratio 4
Hence, 7th term of GP,
x(4)6 = 4096
x = 1 or 1 million.
96. The price of raw materials has gone up by 15%, labor cost has also increased from 25% of the cost of raw material to 30% of the cost of raw material. By how much percentage should there be reduction in the usage of raw materials so as to keep the cost same?
a) 28%
b) 17%
c) 27%
d) 24%
Discussion
Explanation: Let the initial cost of raw material be 100. So, initial labor cost was 25 and net cost was 125
15% increment in raw materials cost and labor cost has gone up to 30% from 25 %
Raw material cost = 115
Labor cost = (115 × 30%) = 34.5
So, New net cost = 115 + 34.5 = 149.5
Difference of labor cost = 149.5 - 125 = 24.5
% reduction = $$\frac{{24.5 \times 100}}{{149.5}}$$ = 17%(approx.)
97. A sales executive gets 20% bonus of the total sales value and 10% commission besides the bonus on the net profit after charging such commission. If the total sales value be Rs. 10 lakh per annum and the total profit of the company be Rs. 1.32 lakh, then his total earning per annum will be, given that he is not entitled to receive any fixed salary from the company
a) 2.3 lakh
b) 2.32 lakh
c) 2.12 lakh
d) None of these
Discussion
Explanation:
$$\eqalign{ & {\text{His bonus}}, \cr & = \frac{{ {20 \times 1000000} }}{{100}} \cr & = 2\, \text{lakh} \cr & {\text{Total}}\,{\text{profit}} = {\text{Net}}\,{\text{profit}} + \frac{{ {10 \times {\text{net}}\,{\text{profit}}} }}{{100}} \cr & 1.32\,\text{lakh} = {\text{Net}}\,{\text{profit}} \times \left[ {1 + {\frac{{10}}{{100}}} } \right] \cr & {\text{Net}}\,{\text{profit}} = \frac{{132000}}{{1.1}} = 120000 \cr & {\text{Commission}} = \left( {{\text{Total}}\,{\text{profit}} - {\text{Net}}\,{\text{profit}}} \right) \cr & = 132000 - 120000 \cr & = 12000 \cr & {\text{Hence}}, {\text{his}}\,{\text{total}}\,{\text{earnings}} \cr & = 2\,\text{lakh} + 12000 \cr & = Rs.\,212000 \cr} $$
98. A shepherd had n goats in the year 2000. In 2001 the no. of goats increased by 40%. In 2002 the no. of goats declined to 70%. In 2003 the no. of goats grew up 30%. In 2004, he sold 10% goats and then he had only 34,398 goats. The percentage increase of the no. of goats in this duration was :
a) 16.66%
b) 14.66%
c) 11.33%
d) 20%
Discussion
Explanation: There is no need of the number of goats given i.e. 34,398.
Initially, let there be 100 goats.
100 == 40% ↑==> 140 == 30%↓(declined to 70%) ==> 98 == 30%↑ ==> 127.4 == 10%↓(sold) ==> 114.66
% increase = 14.66% [As 100 becomes 114.66]
99. In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1600 employees, then the no. of female employees who are computer literate ?
a) 690
b) 674
c) 672
d) 960
Discussion
Explanation: Total employees = 1600
Female employees, 60% of 1600
$$ = \frac{{60 \times 1600}}{{100}} = 960$$
Then male employees = 640
50% of male are computer literate,
= 320 male computer literate
62% of total employees are computer literate,
$$ = \frac{{62 \times 1600}}{{100}} = 992$$ computer literate
Female computer literate = 992 - 320 = 672
100. The price of a car depreciates in the first year by 25% in the second year by 20% in third year by 15% and so on. The final price of the car after 3 years, if the present cost of the car is Rs. 10,00,000 :
a) 7,80,000
b) 1,70,000
c) 6,90,000
d) 5,10,000
Discussion
Explanation: Price after third depreciation,
100 ==25%↓ ==> 75 == 20%↓==>60 == 15% ↓ ==> 51
The price will be,
= Rs. 5,10,000