1. 30% of a number when subtracted from 91, gives the number itself. Find the number.

a) 60

b) 65

c) 70

d) 75

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

2. 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) $$84\frac{4}{5}\% $$

Explanation: Let the third number be 100. Then,

1

^{st}number = 130

2

^{nd}number = 140

% 1

^{st}number to the 2

^{nd}number

$$\eqalign{ & = \frac{{130 \times 100}}{{140}} \cr & = \frac{{650}}{7} \cr & = 92\frac{6}{7}\% \cr} $$

3. 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%

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 = $$\frac{{128}}{{200}} \times 100 = 64\% $$

4. 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

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

5. 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

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.

6. 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

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

7. 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%

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 = $$\frac{{120 \times 100}}{{125}} = 96\% $$

8. 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

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

9. 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

Explanation: 100000 == 10%↑(1

^{st}year) ==> 110000 == 10%↑(2

^{nd}year) ==> 121000

Population at starting of 3

^{rd}year = 121000

10. 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

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.