Percentage
Q21. If the price of pencil is reduced by 20%, a person can buy 2 more pencils for a rupee. How many pencils are available for a rupee ?
(a) 5
(b) 8
(c) 12
(d) 18
Answer: (b) 8
Let no. of pencils be available for a rupee be n
Reduced Price = (80/100) X 1 = Rs. 4/5
4/5 rupee fetch n pencils
∴ 1 rupee fetch = n X (5/4) pencil
∴ 5n/4 = n+2
⇒ 5n = 4n + 8
⇒ n = 8
Q22. A number is first increased by 40% and then reduced by 40%. What would be the percentage change in the number ?
(a) 12%
(b) 16%
(c) 19%
(d) 21%
Answer: (b) 16%
Let the number be 100
∴ Final Value = 60% of 140% of 100 = (60/100) X (140/100) X 100 = 84
Change = 16% decrease
Q23. How is ½% expressed as a decimal fraction ?
(a) 0.005
(b) 0.010
(c) 0.015
(d) 0.050
Answer: (a) 0.005
½% = ½/100 = 1/200 = 0.005
Q24. y% of y is the same as 10% of
(a) y/10
(b) y2/10
(c) y/100
(d) y2/100
Answer: (b) y2/10
Let, the required number be a
A/Q y% of y = 10% of a
⇒ (y/100) X y = (10/100) X a
⇒ y2 = 10a
⇒ a = y2/10
Q25. 12% of 980 - ? % of 450 = 30% of 225
(a) 103/17
(b) 111/15
(c) 117/17
(d) 167/15
Answer: (d) 167/15
Let, the required number be x
A/Q 12% of 980 - ? % of 450 = 30% of 225
⇒ (12/100) X 980 - (x/100) X 450 = (30/100) X 225
⇒ 11760 - 450x = 6750
⇒ 450x = 5010
⇒ x = 167/15
Q26. 20% of a number is less than 15% of 550 by 10. The number is
(a) 215/2
(b) 577/2
(c) 807/2
(d) 925/2
Answer: (d) 925/2
Let, the required number be x
A/Q 20% X x = 15% of 550 + 10
⇒ | 20x | = | 15 | X 550 + 10 |
100 | 100 |
⇒ | x | = | 165 | + 10 |
5 | 2 |
⇒ x = 5 ( | 165 + 20 | ) |
2 |
⇒ x = 5 X (185/2) = 925/2
Q27. Two numbers are less than a third number by 30% and 37% respectively. How much percent is the second number less than the first ?
(a) 10%
(b) 20%
(c) 35%
(d) 40%
Answer: (a) 10%
Let, the 3rd number be x
∴ 1st number = x - (30x/100) = 70x/100
2nd number = x - (37x/100) = 63x/100
1st number - 2nd number = | 70x | - | 63x | = | 7x |
100 | 100 | 100 |
Required % = | 7x/100 | X 100 = | 7x | X 100 = 10% |
70x/100 | 70x |
Q28. How is 2/5 expressed as percentage ?
(a) 20%
(b) 30%
(c) 40%
(d) 50%
Answer: (c) 40%
Required percentage = (2/5) X 100% = 40%
Q29. Out of an earning of Rs. 800 a man spends 60%. How much does he save ?
(a) Rs. 140
(b) Rs. 270
(c) Rs. 320
(d) Rs. 410
Answer: (c) Rs. 320
Speed = 60%
∴ Save = 40%
Required amount = Rs. 800 X 40% = Rs. 800 X (40/100) = Rs. 320
Q30. 10% of the voters in an election did not cast their votes. In the election, there were only two candidates. The winner by obtaining 50% of the total votes defeated his contestent by 1100 votes. The total number of voters in the election was.
(a) 5000
(b) 6500
(c) 8000
(d) 11000
Answer: (d) 11000
Let, the total number of voters be x
Votes cast = 90% of x = (90/100) X x = 9x/10
Votes in favour of winning candidates = 50% of x = (50/100) X x = x/2
Votes polled by defeated candidates = (9x/10) - (x/2) = (9x-5x)/10 = 2x/5
A/Q | x | - | 2x | = 1100 |
2 | 5 |
⇒ | 5x - 4x | = 1100 |
10 |
⇒ x = 1100 X 10 = 11000