Practice MCQ Questions and Answer on Percentage

561.

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

562.

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

Solution: 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 Hence, clock lost = 0.42 hours = 25.2 minutes or 25 minute 12 seconds Thus, correct time = 11 : 34 : 48

563.

An empty fuel tank of a car was filled with A type petrol. When the tank was half-empty, it was filled with B type petrol. Again when the tank was half-empty, it was filled with A type petrol. When the tank was half-empty again, it was filled with B type petrol. What is the percentage of A type petrol at present in the tank ?

(A) 37.5%
(B) 35.5%
(C) 30%
(D) 60%

Solution: Let the capacity of the tank be 100 litres. Then, Initially : A type petrol = 100 litres After first operation : A type petrol = $(\frac{100}{2})$ = 50 litres ; B type petrol = 50 litres After second operation : A type petrol = $(\frac{50}{2} + 50)$ = 75 litres B type petrol = $(\frac{50}{2})$ = 25 litres After third operation : A type petrol = $(\frac{75}{2})$ = 37.5 litres B type petrol = $(\frac{25}{2} + 50)$ = 62.5 litres ∴ Required percentage = 37.5%

564.

The income of a company increases 20% per annum. If its income is Rs. 2664000 in the year 2012. Then its income in the year 2010 was :

(A) Rs. 2120000
(B) Rs. 1850000
(C) Rs. 2820000
(D) Rs. 2855000

Solution: Let the income in 2010 be P ⇒ R = 20% ⇒ Income of year 2012 ⇒ Rs. 2664000 $\begin{aligned} \Rightarrow Income of 2012 = P {[1 + \frac{R}{100}]}^{2} \\ \Rightarrow 2664000 = P {[1 + \frac{20}{100}]}^{2} \\ \Rightarrow 2664000 = P \times \frac{6}{5} \times \frac{6}{5} \\ \Rightarrow Income in 2010 = 1850000 \end{aligned}$

565.

In an election 4% of the votes caste become invalid. Winner gets 55% of casted votes and wins the election by a margin of 4800 votes. Find the total number of votes casted.

(A) 45000
(B) 48000
(C) 50000
(D) 52000

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% = 4800 So, 1% = $\frac{4800}{9.66}$ Thus, 100% Votes = $\frac{4200 \times 100}{9.66}$ = 50000 Hence, Total Voters = 50000 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, $= \frac{0.96 \times 55}{100} = 0.528 x$ votes Loser gets = (0.96X - 0.528X) = 0.432X Difference = 0. 528 - 0.432 = 0.096X 0.096X = 4800 X = 50000

566.

In an election between two candidates, the defeated candidate secured 42% of the valid votes polled and lost the election by 7,68,400 votes. If 82,560 votes were declared invalid and 20% people did NOT cast their vote, then the invalid votes were what percentage (rounded off to 1 decimal place) of the votes which people did NOT cast?

(A) 10.6%
(B) 9.8%
(C) 12.9%
(D) 6.8%

Solution: Total number of votes = 5x Votes polled = 4x Valid votes = 4x - 82560 Invalid votes = 82560 Defeated candidate = 42% of valid votes Winning n = 58% of valid votes 16% of valid votes (difference) = 768400 16%(4x - 82560) = 768400 4x = 4802500 + 82560 x = 1221265 $\begin{aligned} Required % = \frac{Invalid votes}{Number of people not voted} \times 100 \\ = \frac{82560}{1221265} \times 100 \\ = 6.76 % ≅ 6.8 % \end{aligned}$

567.

Find the : 38% of 341 = ?

(A) 120.68
(B) 129.58
(C) 135.78
(D) 136.28

Solution: = 38% of 341 = $\frac{38}{100}$ × 341 = $\frac{12958}{100}$ = 129.58

568.

A shopkeeper first raises the price of Jewellery by x% then he decreases the new price by x%. After such up down cycle, the price of a Jewellery decreased by Rs. 21025. After a second up down cycle the Jewellery was sold for Rs. 484416. What was the original price of the jewellery.

(A) Rs. 5,26,000
(B) Rs. 6,00,625
(C) Rs. 5,25,625
(D) Rs. 5,00,000

Solution: Let the initial price = Rs. 10000p Price after first increment = 10000p + 100xp Price after first decrement = 10000p + 100xp - (100px + px2) = 10000p - px2 Now, total decrement, px2 = 21025 . . . . . (1) Price after second increment, = 10000p - px2 + 100xp - $\frac{p x^{3}}{100}$ Price after second increment, = 10000p - p2 + 100xp - $\frac{p^{3}}{100}$ - 100xp + $\frac{p x^{3}}{100}$ - px2 + $\frac{p x^{4}}{10000}$ = 10000p - 2px2 + $\frac{p x^{2}}{10000}$ = 484416 . . . . . . (2) On solving equation (1) and (2), We get x = 20 Substituting back we get, p = 5,25,625

569.

Two numbers are respectively 20% and 50% of the third number. What percent is the first number of the second ?

(A) 10%
(B) 20%
(C) 30%
(D) 40%

Solution: Let the 3rd number is 100 According to the question, $\begin{aligned} 1^{st} 2^{nd} 3^{rd} \\ 20 : 50 : 100 \end{aligned}$ Required % = $\frac{20}{50}$ × 100 = 40%

570.

The price of a car depreciates in the first year by 25% in the second year by 20% in third year by 15% and so on. The final price of the car after 3 years, if the present cost of the car is Rs. 10,00,000 :

(A) 7,80,000
(B) 1,70,000
(C) 6,90,000
(D) 5,10,000

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Practice MCQ Questions and Answer on Percentage

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