Percentage Aptitude Solved Examples - Set 01

Question No. 01
Rajeev buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.
(A) Rs. 6876.10
(B) Rs. 6999.20
(C) Rs. 6654
(D) Rs. 7000
Answer: Option A
Explanation:
Rebate = 6% of Rs. 6650 = Rs. (6/100) × 6650 = Rs. 399
Sales tax = 10% of Rs. (6650 - 399) = Rs. (10/100) × 6251 = Rs. 625.10
∴ Final amount = Rs. (6251 + 625.10) = Rs. 6876.10

Question No. 02
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
= {(45/100) × 6000} = 2700

Question No. 03
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
(60/100) × x = 420
=> (420 × 100)/60 = 700

Question No. 04
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) None of these
Answer: Option D
Explanation:
x% of y = {(x/100) × y} = {(y/100) × x} = y% of x
∴ A = B

Question No. 05
A student multiplied a number by 3/5 instead of 5/3. 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 = (5/3)x - (3/5)x = (16/15)x
Error% = [(16x/15) × (3/5x) × 100] % = 64%

Question No. 06
What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
(A) 1
(B) 14
(C) 20
(D) 21
Answer: Option C
Explanation:
Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number =14
∴ Required percentage = {(14/70) × 100} % = 20%

Question No. 07
Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
(A) 57%
(B) 60%
(C) 65%
(D) 90%
Answer: Option A
Explanation:
Total number of votes polled = (1136 + 7636 + 11628) = 20400
∴ Required percentage = {(11628/20400) × 100} % = 57%

Question No. 08
Ankit 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)
=> [(30/100) × (100/6) = 5
∴ Cost of tax free items = Rs. [25 - (5 + 0.30)] = Rs. 19.70

Question No. 09
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 = (56/100) (x + 9 + x)
=> 25(x + 9) = 14(2x + 9)
=> 3x = 99
=> x = 33
So, their marks are 42 and 33

Question No. 10
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
=> b = (20/100) a = b
b% of 20 = {(b/100) × 20} = [{(20/100) a} × {(1/100) × 20}] = {(4/100) a} = 4% of a

Percentage Aptitude:
Formula:                Percentage Aptitude Formulas
Solved Examples:  Solved Examples: Set 01
Practice Test:         Practice Test: 01     Practice Test: 02
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