Percentage
Q11. A reduction of 20% in the price of rice enables a person to buy 3.5 Kg more rice for Rs. 385. The original price of the rice is
(a) Rs. 25.50 /Kg
(b) Rs. 26 /Kg
(c) Rs. 27.50 /Kg
(d) Rs. 28.50 /Kg
Answer: (c) Rs. 27.50 /Kg
Let, the original price of rice be Rs. x per Kg
New price of 1 Kg rice = Rs.(x - (20/100) X x) = Rs. (x - x/5) = Rs. 4x/5
A/Q | 5 X 385 | - | 385 | = 3.5 |
4x | x |
⇒ | 1925 - 1540 | = 3.5 |
4x |
⇒ | 385 | = 3.5 |
4x |
⇒ x = 385/(4X3.5) = 27.5 = Rs. 27.50/Kg
Q12. The quantity of water that should be added to reduce 10ml lotion containing 60% alcohol to a lotion containing 40% alcohol is
(a) 5 ml
(b) 8 ml
(c) 11 ml
(d) 13 ml
Answer: (a) 5 ml
Alcohol in 10ml lotion = (60/100) X 10 ml = 6 ml
Water in it = 10ml - 6ml = 4 ml
Let x ml of water be added to it
Now | 6 | = 40% |
10 + x |
⇒ | 6 | = | 40 | = | 2 |
10 + x | 100 | 5 |
⇒ 20 + 2x = 30
⇒ 2x = 10
⇒ x = 5 ml
Q13. In two successive years, 200 and 150 students of a school appeared at the final examination. Respectively 70% and 60% of them passed. The average rate of pass is
(a) 63.25%
(b) 65.12%
(c) 65.71%
(d) 66.10%
Answer: (c) 65.71%
Total candidates = 200 + 150 = 350
Total passed = 200 X | 70 | + 150 X | 60 |
100 | 100 |
= 140 + 90 = 230
Pass% = (230/350) X 100 = 65.71%
Q14. In two successive years, 100 and 80 students of a school appeared at the final examination. Respectively 75% and 60% of them passed. Teh average rate of fail is
(a) 28.75%
(b) 31.66%
(c) 32.54%
(d) 37.45%
Answer: (b) 31.66%
Total candidate = 100 + 80 = 180
Total passed = 100 X | 75 | + 80 X | 60 |
100 | 100 |
= 75 + 48 = 123
Total failed = 180 - 123 = 57
Fail% = (57/180) X 100 = 31.66
Q15. The price of petrol is increased by 20%. By how much percent a car owner should reduce his consumption of petrol so that the expenditure on the petrol would not be increased ?
(a) 13(2/3)%
(b) 14(1/5)%
(c) 16(2/7)%
(d) 16(2/3)%
Answer: (d) 16(2/3)%
Reduction % in consumption = { | r | X 100 }% |
100 + r |
= | 20 | X 100 % = | 200 | % = 16 | 8 | % = 16 | 2 | % |
120 | 12 | 12 | 3 |
Q16. After reducing the salary of a man by 50% and subsequently it is increased by 40%. The loss is
(a) 10%
(b) 20%
(c) 25%
(d) 30%
Answer: (d) 30%
Let the salary of the man be Rs. 100
After reducing salary = 100 - 100 X(50/100) = Rs. 50
After increasing salary = Rs. 50 + 50 X (40/100) = Rs. 70
∴ Loss% = 100% - 70% = 30%
Q17. 10% of the electorate did not cast their votes in an election between two candidates. 10% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 1620 votes. The number of voters enrolled on the voters list was
(a) 15000
(b) 18000
(c) 22000
(d) 25000
Answer: (d) 25000
Let the number of voters enrolled be x
Votes cast = (90/100) X x = 9x/10
Valid votes = 90% of | 9x | = | 90 | X | 9x | = | 81x |
10 | 100 | 10 | 100 |
Votes polled by successful candidate = | 54 | X | 81x | = | 4374x |
100 | 100 | 10000 |
Votes polled by defeated candidate = | 46 | X | 81x | = | 3726x |
100 | 100 | 10000 |
4374x - 3726x = 16200000
⇒ x = 25000
Q18. The sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, then the numbers are
(a) 1025
(b) 1158
(c) 1411
(d) 1735
Answer: (c) 1411
Let, the numbers be x and 2490 - x
Now 6.5% of x = 8.5% of (2490 - x)
⇒ 6.5x/100 = 8.5/100 (2490 - x)
⇒ 65x/100 = 85/100(2490 - x)
⇒ 65x = 85 X 2490 - 85x
⇒ 150x = 85 X 2490
⇒ x = 1411
Q19. In measuring the sides of a rectangle errors of 5% and 3% in excess are made. The error percent in the calculated area is
(a) 5.25%
(b) 8.15%
(c) 9.12%
(d) 11.23%
Answer: (b) 8.15%
Let, length = x units
breadth = y units
∴ Actual area = xy sq. units
Length shown = (105/100) X x =21x/20 units
Breadth shown = (103/100) X y = 103y/100 units
Calculated area = (21x/100) X (103y/100) sq. unit = 2163xy/2000 sq. unit
Error = 2163xy/2000 - xy = 163xy/2000
Error % = | 163xy | X | 1 | X 100% = | 163 | % = 8.15% |
2000 | xy | 20 |
Q20. Of the 1000 inhabitants of a town, 60% are females of whom 20% are literate. If of all the inhabitants 25% are literate, then what percent of the males of the town are literate
(a) 32.5%
(b) 33.4%
(c) 35.9%
(d) 42.5%
Answer: (a) 32.5%
Females = (60/100) X 1000 = 600
Males = 1000 - 600 = 400
Literate Females = (20/100) X 600 = 120
Total literates = (25/100) X 1000 = 250
∴ Male literates = 250 - 120 = 130
∴ Required % = (130/400) X 100% = 32.5%
Practice Test Exam