## Percentage Questions and Answers Part-8

1. 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

Answer: c
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}

2. 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

Answer: b
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

3. 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

Answer: b
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

4. 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

Answer: b
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}

5. (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

Answer: c
Explanation:
\eqalign{ & {\frac{{XY}}{{100}}} + {\frac{{YX}}{{100}}} \cr & = \frac{{2XY}}{{100}} \cr & = 2\% \,of\,XY \cr}

6. 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

Answer: d
Explanation: 100 === 25% ↑===> 125 ===> 20% ↓===> 100
So, there is no change in the area of rectangle

7. 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%

Answer: b
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 = $$= \frac{{10 \times 100}}{{140}} = 7.14\%$$

8. 220% of a number X is 44. What is 44% of X.
a) 8.8
b) 8.9
c) 6.6
d) 7.7

Answer: a
Explanation: 220% of X = 44
X = 20
Thus, 44% of 20
$$= \frac{{44 \times 20}}{{100}} = 8.8$$

9. 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

Answer: c
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 $$= \frac{{1250 \times 100}}{{10000}} = 12.5\%$$

10. 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) $$\frac{{100}}{{y \times \left( {z - 1} \right)}}\,{\text{days}}$$

Answer: c
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}