Percentage

Question:
If A = x% of y and B = y% of x, then which of the following is true?

[A].

A is smaller than B.

[B].

A is greater than B

[C].

Relationship between A and B cannot be determined.

[D].

If x is smaller than y, then A is greater than B.

Answer: Option E

Explanation:

x% of y =		x	x y		=		y	x x		= y% of x
		100					100

A = B.

Question:
If 20% of a = b, then b% of 20 is the same as:

[A].

4% of a

[B].

5% of a

[C].

20% of a

[D].

None of these

Answer: Option A

Explanation:

20% of a = b	20	a = b.
	100

b% of 20 =		b	x 20		=		20	a x	1	x 20		=	4	a = 4% of a.
		100					100		100				100

Question:
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

Answer: Option C

Explanation:

Let their marks be (x + 9) and x.

Then, x + 9 =	56	(x + 9 + x)
	100

25(x + 9) = 14(2x + 9)

3x = 99

x = 33

So, their marks are 42 and 33.

Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is of the number of students of 8 years of age which is 48. What is the total number of students in the school?
[A].

72

[B].

80

[C].

120

[D].

150

Answer: Option E

Explanation:

Let the number of students be x. Then,

Number of students above 8 years of age = (100 – 20)% of x = 80% of x.

80% of x = 48 +	2	of 48
	3

	80	x = 80
	100

x = 100.

Video Explanation: https://youtu.be/yPfocU6DA2M

Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:

[A].

2700

[B].

2900

[C].

3000

[D].

3100

Answer: Option A

Explanation:

Number of valid votes = 80% of 7500 = 6000.

Valid votes polled by other candidate = 45% of 6000

=		45	x 6000		= 2700.
		100

Question: A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
[A].

588 apples

[B].

600 apples

[C].

672 apples

[D].

700 apples

Answer: Option D

Explanation:

Suppose originally he had x apples.

Then, (100 – 40)% of x = 420.

	60	x x = 420
	100

x =		420 x 100	= 700.
		60

Video Explanation: https://youtu.be/-Pv25Do3WwY

Question: A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
[A].

45%

[B].

45	5	%
	11

[C].

54	6	%
	11

[D].

55%

Answer: Option B

Explanation:

Number of runs made by running = 110 – (3 x 4 + 8 x 6)

= 110 – (60)

= 50.

Required percentage =		50	x 100	% = 45	5	%
		110			11

Video Explanation: https://youtu.be/X2zTnABqEHU

Question: Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?

[A].

Rs. 15

[B].

Rs. 15.70

[C].

Rs. 19.70

[D].

Rs. 20

Answer: Option C

Explanation:

Let the amount taxable purchases be Rs. x.

Then, 6% of x =	30
	100

x =		30	x	100	= 5.
		100		6

Cost of tax free items = Rs. [25 – (5 + 0.30)] = Rs. 19.70

Question:
What is the percentage error in the calculation?
[A].

34%

[B].

44%

[C].

54%

[D].

64%

Answer: Option D

Explanation:

Let the number be x.

Then, error =	5	x –	3	x =	16	x.
	3		5		15

Error% =		16x	x	3	x 100	% = 64%.
		15		5x

Question:
The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:

[A].

4.37%

[B].

5%

[C].

6%

[D].

8.75%

Answer: Option B

Explanation:

Increase in 10 years = (262500 – 175000) = 87500.

Increase% =		87500	x 100	% = 50%.
		175000

Required average =		50	% = 5%.
		10