## Percentage Questions and Answers Part-1

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%

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%

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%

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%

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

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%

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

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) $$\frac{{y - x}}{2}$$

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%

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%

Now, % increase in population = $$\frac{{4.04}}{{100}} \times 100 = 4.04\%$$