Percentages: Solved Examples

Q1. A student obtained 62.5 % marks in a certain examination. If the maximum marks are 800. Find the total marks obtained by her.
A. 525
B. 600
C. 375
D. 500
Sol: Option C
Solution: 800 * 62.5/100 = 500
Q2. The annual sales of company B were Rs 96,000 in fiscal year 95-96 and Rs 1,08,000 in fiscal 96-97. What was the % increase in turnover?
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A. 16.67 %
B. 62.5 %
C. 40 %
D. 12.5 %
Sol: Option D
Solution: Increase = 96,000 – 1,08, 000 = 12,000
∴ % Increase = 12000 * 100/96000 = 100 * 1/8 = 12.5 %
Q3. The price of a Bajaj Scooter is Rs 25,000 which is 20 % lesser than a LML Scooter. What is the price of a LML Scooter?
A. 15250
B. 31250
C. 40150
D. 75230
Sol: Option B
Solution: Here note that the % given is defined in terms of the price of LML Scooter and not Bajaj Scooter. ∴ Computing the price of SMS as 1.2 times Bajaj's price will give incorrect answer. The data given is:
LML * (100 – 20)/100 = Bajaj = 25,000
∴ LML =25,000 × 100/80 = Rs 31,250
Or you can simply do = 25,000/0.8 = 31250
(20 % less means it is 0.80 times of the other one)
Q4. The price of rice increases by 30 %. In order to keep the expenses on rice constant as before, by what percentage should a person cut down his consumption?
A. 22/3 %
B. 31/5 %
C. 67/3 %
D. 23/11 %
Sol: Option C
Solution: Applying the formula 100 * R/ (100 + R),
Since the price has increased, the consumption should be reduced by:
(100 * 30)/ (100+130) = 22 1/3 %
Q5. Tom’s income is 20 % less than Jerry’s. How much is Jerry’s income more than Tom’s?
A. 25 %
B. 60 %
C. 45 %
D. 30 %
Sol: Option A
Solution: Applying the formula 100 * R/(100 - R)
As , income is 20% less
Jerry’s income is more by = 100 * 20/80 = 25 %
Q6. A traveling salesman carried 75 % of his money in traveler’s cheque and 25 % in cash. During one of his journeys, he lost his entire cash and spent from his traveler’s cheque. On completion of the journey, he returned 30% of the traveler’s cheque, which amounted to Rs 180. What was the total money that he carried?
A. Rs 500
B. Rs 600
C. Rs 450
D. Rs 800
Sol: Option D
Solution: 30 % of Traveler’s Cheque = Rs 180
∴ 100 % of Traveler's Cheque = 180 * 100/30 = Rs 600
Since Traveler's Cheque accounted for 75% of the total money that he had carried, the total money that he carried is: 600 * 100/75 = Rs 800
Q7. A number is increased by 20%, and then it is decreased by 30%, what is the net change in the number?
A. 16 % increase
B. 16 % decrease
C. 10 % decrease
D. 5 % increase
Sol: Option B
Solution: Using the formula: X + Y + XY/100
⇒ 20 + (-30) + 20 *-30 /100 = -16
This means there is a decrease of 16 %
Q8. A square is converted into a rectangle by increasing one of its sides by 5 % and reducing the other by 5 %. What will be the % change in the area of the two figures?
A. 0.5 % decrease
B. 0.5 % increase
C. 0.25 % increase
D. 0.25 % decrease
Sol: Option D
Solution: Let the side of the square = a
∴ Its area = a2; When the square is being converted to a rectangle, the length becomes 1.05a and the width becomes 0.95a. ∴ New area = 1.05a × 0.95a = 0.9975a2
Change in area = a decrease of 0.0025a2
∴ % decrease in area =0.0025a2 * 100/a2= 0.25 %
Q9. In an election there were two candidates P and S. The poll turnout was only 90 %. 500 of the given votes were declared invalid. P won by a margin of 400 votes and got 440/9 % of the total votes. Find the total number of eligible voters and the number of votes received by each of the candidates.
A. 5000,2200, 1800
B. 6000,1200,3800
C. 4000,1100,3500
D. 4500,2200,1000
Sol: Option A
Solution: Let the registered voters = X
P got 440/9 % of X = 440/9 % of X = 4.49X/9
Since P got 400 votes more than S, S got 4.4X/9 – 400
Total votes registered = X = P + S + Invalid votes
X = 4.4 X/9 + (4.4 X/9 – 400)+ 500 ⇒ X = 8.8X/9 + 100
⇒ X = 4500. Since the poll turnout was only 90%, the total number of eligible voters = 100/90 * 4500 = 5000
Number of votes P got = 4.4/9 * 4500 = 2200
Number of votes S got = 2200 – 400 = 1800.
Q10. If the population of a town is 926100 and it has been growing annually at 5 %, what was the population 3 years ago?
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A. 200,000
B. 600,000
C. 400,000
D. 450,000
Sol: Option A
Let the population be X
X * (100 + 5)3 / (100) 3 =926100 %rArr; X * (105/ 100) * (105/100) * (105/100) = 926100
⇒ X * (21/20) * (21/20) * (21/20) = 926100
⇒ X = 926100 * (20/21) * (20/21) * (20/21) = 8, 00, 00