# Percentages Quiz Set 008

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 Correct Answers: Wrong Answers: Unattempted:

### Question 1

If 20% of X is Y, then Y% of 20 is?

A

4 % of X.

B

14 % of X.

C

34 % of X.

D

24 % of X.

Soln.
Ans: a

We have Y = \$(20 × X)/100\$, so Y% of 20 is same as \$(20 × X)/100\$% × 20, which can be rearranged to \$(20 × 20)/100\$% × X = 4% of X.

### Question 2

Two numbers are, respectively, 5% and 35% less than a third number. What percent is the second of the first?

A

\$68{8/19}\$ %.

B

\$73{5/18}\$ %.

C

61 %.

D

\$64{13/21}\$ %.

Soln.
Ans: a

If the third number is 100, first number is (100 - 5) = 95, and the second number is (100 - 35) = 65. The required ratio is \$65/95\$ × 100 = \${1300/19}\$, which is same as: \$68{8/19}\$%.

### Question 3

If 11% of A + B = 18% of A - B, then what percent of B is A?

A

\$4{1/7}\$ %.

B

6 %.

C

\$2{4/9}\$ %.

D

\$5{5/9}\$ %.

Soln.
Ans: a

We have been given 11% of A + B = 18% of A - B, so \${A + B}/{A - B}\$ = \$18/11\$. By componendo and dividendo, \${(A + B) + (A - B)}/{(A + B) - (A - B)}\$ = \${18 + 11}/{18 - 11}\$, which gives \$A/B\$ = \$29/7\$ = \${29/7}\$, which is same as: \$4{1/7}\$%

### Question 4

A sample of alcohol has 80% water, and another sample has 70% water. If equal volumes of both the samples are combined, what is the percentage of water in the new sample?

A

75 %.

B

77 %.

C

73 %.

D

79 %.

Soln.
Ans: a

If 100 units of both alcohol are combined, there will be 150 units of water in 200 units of the new sample. The percentage of water is \$150/200\$ × 100 = 75%.

### Question 5

A number is first increased by 100%, and thereafter it is reduced by 100% again. What is the overall reduction?

A

100 %.

B

102 %.

C

98 %.

D

104 %.

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\$ = 100%

This Blog Post/Article "Percentages Quiz Set 008" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-05-17.

Posted by Parveen(Hoven),
Aptitude Trainer

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