Percentages Quiz Set 005

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Question 1

One number is 300 more than the other, and it is 75% of the sum of them. What is the number?

 A

450.

 B

550.

 C

350.

 D

650.

Soln.
Ans: a

Let the numbers be x and x - 300. We have been given x = $75/100$ × (x + x - 300), which gives 100x = 75 × (2x - 300), solving, we get x = 450.


Question 2

A number is first increased by 20%, and thereafter it is reduced by 20% again. What is the overall reduction?

 A

4 %.

 B

6 %.

 C

10 %.

 D

8 %.

Soln.
Ans: a

Let us derive the shortcut formula first, so that you can remember it and use it when the need arises. Suppose the number is 100, and let the increase be x%. The number becomes 100 + x. When it is reduced by x%, we get 100 + x - $((100 + x) × x)/100$ = 100 + x - $(x + x^2/100)$ = 100 - $x^2/100$, hence a reduction of $x^2/100$ = 4%


Question 3

A clerk multiplied a number by 2/1 instead of 1/2. What is the percentage of error?

 A

75 %.

 B

77 %.

 C

73 %.

 D

79 %.

Soln.
Ans: a

If the actual figure is x, the error is ${2x}/1$ - ${1x}/2$ = ${2^2x - 1^2x}/{2 × 1}$ = ${3x}/2$, so %-error = ${(3x)/2}/{(2x)/1}$ × 100 = ${3 × 1}/{2 × 2}$ × 100 = 75%.


Question 4

The age of Mr. X is 80% more than Mr. Y's age which is 20 years at present. By what percent is Y's age less than Mr. X's age?

 A

$44{4/9}$ %.

 B

$51{1/8}$ %.

 C

$35{6/11}$ %.

 D

$38{9/11}$ %.

Soln.
Ans: a

Age of Mr. X is 20 + ${80 × 20}/100$ = 36 years. Mr. Y's age is less than Mr. X's age by ${80 × 20}/100$ = 16 years. In terms of percentage, it is $16/36$ × 100 = ${400/9}$, which is same as: $44{4/9}$.


Question 5

One number is 160 more than the other, and it is 70% of the sum of them. What is the number?

 A

280.

 B

380.

 C

180.

 D

480.

Soln.
Ans: a

Let the numbers be x and x - 160. We have been given x = $70/100$ × (x + x - 160), which gives 100x = 70 × (2x - 160), solving, we get x = 280.


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This Blog Post/Article "Percentages Quiz Set 005" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-04-07.

Posted by Parveen(Hoven),
Aptitude Trainer


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