Practice MCQ Questions and Answer on Percentage

111.

Two discount of 8% and 12% are equal to a single discount of:

(A) 20%
(B) 19.04%
(C) 22.96%
(D) 22%

112.

The population of a town is 1771561. If it had been increasing at 10% per annum, its population 6 years ago was :

(A) 1000000
(B) 1100000
(C) 1210000
(D) 1331000

Solution: Population of 6 years ago : $\begin{aligned} = [\frac{1771561}{{(1 + \frac{10}{100})}^{6}}] \\ = 1771561 \times {(\frac{10}{11})}^{6} \\ = \frac{1771561 \times 1000000}{1771561} \\ = 1000000 \end{aligned}$

113.

One-fourth of sixty percent of a number is equal to two-fifth of twenty percent of another number. What is the respective ratio of the first number to the second number ?

(A) 4 : 7
(B) 5 : 9
(C) 8 : 13
(D) Cannot be determined

Solution: Answer & Solution Answer: Option E Solution: Let the first number be x and the second number be y $\frac{1}{4} of 60% of x = \frac{2}{5} of 20% of y$ $\begin{aligned} \Rightarrow \frac{1}{4} \times \frac{60}{100} \times x = \frac{2}{5} \times \frac{20}{100} \times y \\ \Rightarrow \frac{3 x}{20} = \frac{2 y}{25} \\ \Rightarrow \frac{x}{y} = \frac{2}{25} \times \frac{20}{3} \\ \Rightarrow \frac{x}{y} = \frac{8}{15} \end{aligned}$

114.

The price of an article was increased by r%. Later the new price was decreased by r%. If the latest price was Rs. 1, then the original price was :

(A) Rs. 1
(B) Rs. $\frac{1 - r^{2}}{100}$
(C) Rs. $\frac{\sqrt{1 - r^{2}}}{100}$
(D) Rs. $(\frac{10000}{10000 - r^{2}})$

Solution: r% = $\frac{r}{100}$ Initial Price Final 100 (100 + r) 100 (100 - r) 10000 (100 + r) (100 - r) According to the question, (100 + r) (100 - r) units = Rs. 1 (10000 - r2) units = Rs. 1 1 unit = $(\frac{1}{10000 - r^{2}})$ Original price = $(\frac{10000}{10000 - r^{2}})$

115.

In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is $\frac{2}{3}$ of the number of students of 8 years of age which is 48. What is the total number of students in the school?

(A) 72
(B) 80
(C) 120
(D) 150

Solution: Answer & Solution Answer: Option E Solution: Let the number of students be x. Then, Number of students above 8 years of age $\begin{aligned} = (100 - 20) % of x = 80 % of x \\ ∴ 80 % of x = 48 + \frac{2}{3} of 48 \\ \Rightarrow \frac{80}{100} x = 80 \\ \Rightarrow x = 100 \end{aligned}$

116.

In what ratio must a mixture of 30% alcohol strength be mixed with that of 50% alcohol strength so as get a mixture of 45% alcohol strength ?

(A) 1 : 2
(B) 1 : 3
(C) 2 : 1
(D) 3 : 1

117.

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%

Solution: 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% = $\frac{106 \times 3}{100} = 3.18 cm .$ Decrease in CB = 0.18 cm % decrease = $\frac{0.18}{2} \times 100 = 9 %$ Alternatively, AC = 3 Cm. BC = 2 Cm. Increase in AC by 6%, then New, AC = 3 + 6% of 3 = 3 + 0.18 = 3.18 cm. 0.18 cm increase in AC means 0.18 cm decrease in BC as already mentioned AB as the fixed point. So, % decrease in BC, $\begin{aligned} = \frac{Actual Decrease in BC}{Original BC} \times 100 \\ = \frac{0.18}{2} \times 100 = 9 % \end{aligned}$

118.

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%

Solution: $\begin{aligned} Total number all three got together is, \\ = 1136 + 7636 + 11628 \\ = 20400 \\ % of vote the winning candidate got is, \\ = \frac{11628}{20400} \times 100 \\ = 57 % \end{aligned}$

119.

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

Solution: 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) So, Now this 2 L Consist 80% in puree Thus, total puree will be $\frac{2}{.8} = 2.5 L$

120.

In a factory, the production of cycles rose to 48400 from 40000 in 2 years. The rate of growth per annum is ?

(A) 10.5%
(B) 9%
(C) 8%
(D) 10%

Solution: The production of cycles rose to 48400 from 40000 in 2 years ⇒ Present production = 40000 ⇒ After two years = 48000 ⇒ Time = 2 years ⇒ Rate of increment = ? According to the question, Production after 2 years = Present production ${(1 + \frac{R}{100})}^{t}$ $\begin{aligned} \Rightarrow 48400 = 40000 {(1 + \frac{R}{100})}^{2} \\ \Rightarrow \frac{484}{400} = {(1 + \frac{R}{100})}^{2} \\ \Rightarrow 1 + \frac{R}{100} = \frac{22}{20} \\ \Rightarrow \frac{R}{100} = \frac{1}{10} \\ \Rightarrow R = 10 % \end{aligned}$ ⇔ Rate of increment = 10%

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Practice MCQ Questions and Answer on Percentage

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