Percentages Quiz Set 008

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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%


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Creative Commons License
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 2017-04-07.

Posted by Parveen(Hoven),
Aptitude Trainer


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