Practice MCQ Questions and Answer on Percentage

81.

Ankita's weight is 20% less than that of her grandmother. The grandmother weights 26 kg less than grandmother's husband, whose weight is 81 kg. If Ankita's brother is 8 kg heavier than Ankita, then what is the weight (in kg) of Ankita's brother?

(A) 60
(B) 19
(C) 36
(D) 52

Solution: Grand mother's husband's, weight = 81 kg Grand mother's weight = (81 - 26) kg = 55 kg 20% = $\frac{1}{5}$ Ankita's weight = 55 × $\frac{4}{5}$ = 44 kg Ankita's brother's weight = 44 + 8 = 52 kg

82.

If 0.03 is X% of 0.3, then the value of X is :

(A) 3
(B) 10
(C) 30
(D) Cannot be determined

Solution: X% of 0.3 = 0.03 ⇒ $\frac{X}{100}$ × 0.3 = 0.03 ⇒ X = $\frac{0.03 \times 100}{0.3}$ ⇒ X = 10

83.

In an examination, 34% failed in Mathematics and 42% failed in English. If 20% failed in both the subjects, the percentage of students who passed in both subjects was :

(A) 54%
(B) 50%
(C) 44%
(D) 56%

84.

The price of an articles 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: Let the original price be Rs. $x$ ∴ (100 - r)% of (100 + r)% of $x$ = 1 $\begin{aligned} \Rightarrow \frac{(100 - r)}{100} \times \frac{(100 + r)}{100} \times x \\ \Rightarrow x = \frac{100 \times 100}{(100 - r) (100 + r)} \\ \Rightarrow x = \frac{10000}{(10000 - r^{2})} \end{aligned}$

85.

x * 12 = 75% of 336 Find x.

(A) 27
(B) 25
(C) 21
(D) 19

Solution: $\begin{aligned} 12 x = \frac{75 \times 336}{100} \\ x = \frac{75 \times 336}{100 \times 12} \\ x = 21 \end{aligned}$

86.

In a village three people contested for the post of village Pradhan. Due to their own interest, all the voters voted and no one vote was invalid. The losing candidate got 30% votes. What could be the minimum absolute margin of votes by which the winning candidate led by the nearest rival, if each candidate got an integral percent of votes ?

(A) 4
(B) 2
(C) 1
(D) None of these

Solution: Let total votes in village = 100 Losing candidate got votes = 30% of 100 = 30 votes Winner's and nearer rival's votes = 100 - $\frac{13}{100}$ × 100 = 70 ∴ If both get equal votes then, it should be, 35 ∴ Minimum difference between winner and nearer rival = (36 - 34) = 2

87.

If 50% of (x - y) = 30% of (x + y), then what percent of x is y ?

(A) 25%
(B) $33 \frac{1}{3}$ %
(C) 40%
(D) 400%

Solution: $\begin{aligned} 50 % of (x - y) = 30 % of (x + y) \\ \Rightarrow 5 (x - y) = 3 (x + y) \\ \Rightarrow 5 x - 5 y = 3 x + 3 y \\ \Rightarrow 2 x = 8 y \\ \Rightarrow y = \frac{x}{4} \end{aligned}$ ∴ Required percentage : $\begin{aligned} = (\frac{y}{x} \times 100) % \\ = (\frac{x}{4} \times \frac{1}{x} \times 100) % \\ = 25 % \end{aligned}$

88.

In an election 4% of votes cast are invalid. A candidate gets 55% of casted votes and wins the election by 4200 votes. Find the total number of votes casted.

(A) 30000
(B) 43750
(C) 45000
(D) 42000

Solution: 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% Now, 9.6% = 4200 So, 1% = $\frac{4200}{9.66}$ Thus, 100% Votes = $\frac{4200 \times 100}{9.66}$ = 43750 Hence, Total Voters = 43,750 Alternatively, Let total number of voters were X. Invalid Votes = 4% Valid Votes = 96% Total Valid Votes = 96% of X = $\frac{96 x}{100}$ = 0.96X Winner gets 55% of Valid Votes, = $\frac{0.96 \times 55}{100}$ = 0.528X votes Loser gets = (0.96X - 0.528X) = 0.432X Difference = 0. 528 - 0.432 = 0. 096X 0.096X = 4200 ∴ X = 43750

89.

The charges for a five-day trip by a tourist bus for one full ticket and a half-ticket are Rs. 1440 inclusive of boarding charges which are same for a full ticket and a half-ticket. The charges for the same trip for 2 full tickets and one half-ticket inclusive of boarding charges are Rs. 2220. The fare for a half-ticket is 75% of the full ticket. Find the fare and the boarding charges separately for one full ticket.

(A) Rs. 580, Rs. 400
(B) Rs. 280, Rs. 200
(C) Rs. 480, Rs. 300
(D) Rs. 380, Rs. 400

Solution: Let the fare for a full ticket be Rs. x and the boarding charges be Rs. y per ticket. Then, fare for a half-ticket : = 75% of Rs. x = Rs. $\frac{3 x}{4}$ $\begin{aligned} ∴ (x + y) + (\frac{3}{4} x + y) = 1440 \\ \Rightarrow \frac{7 x}{4} + 2 y = 1440 \\ \Rightarrow 7 x + 8 y = 5760 . . . . . (i) \\ And, 2 (x + y) + (\frac{3}{4} x + y) = 2220 \\ \Rightarrow \frac{11 x}{4} + 3 y = 2220 \\ \Rightarrow 11 x + 12 y = 8880 . . . . . (i i) \end{aligned}$ Solving (i) and (ii), we have, x = 480, y = 300

90.

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

Solution: Let their marks be (x + 9) and x Then, $\begin{aligned} x + 9 = \frac{56}{100} (x + 9 + x) \\ \Rightarrow 25 (x + 9) = 14 (2 x + 9) \\ \Rightarrow 3 x = 99 \\ \Rightarrow x = 33 \end{aligned}$ So, their marks are 42 and 33

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Practice MCQ Questions and Answer on Percentage

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