Aptitude question and answer on Percentage

In this section we are going to discuss about percentage problems. Not just the overview of the topic, but also you are going to learn the important formulas on percentage along with explanation which is easy to understand.

1
When radious of a circle is increased by 100 % , then area of the circle increase by 
A.    200 %
B.    100 %
C.    300 %
D.    400 %

Answer : C.  300 %

Explanation:
\({\pi r^2(4-1) \over \pi r^2} \times 100=300 \%\)

2
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 : D.  700  apples

Explanation:
Suppose originally he had x apples.

Then, (100 - 40)% of x = 420.

=>\({60 \over 100} \times x =420\)

=> \(\bigg ( {420 \times 100 \over 60} \bigg )=700\)

3
If the price of petrol increases by 25% and Benson intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?
A.    8 %
B.    7 %
C.    10 %
D.    6 %

Answer : A.  8 %

Explanation:
Assume that the initial price of 1 Litre petrol = Rs.100 ,Benson spends Rs.100 for petrol,

such that Benson buys 1 litre of petrol

After the increase by 25%, price of 1 Litre petrol = 100×\((100+25)\over100\)=Rs.125

Since Benson spends additional 15% on petrol,

amount spent by Benson = 100×\((100+15)\over 100\)=Rs.115

Hence Quantity of petrol that he can purchase =  \(115 \over125\) Litre

Quantity of petrol reduced = (1−\(115 \over125\)) Litre

Percentage Quantity of reduction = \({(1−{115 \over125})}\over1\)×100

=\(10 \over125\)×100=\(10 \over5\)×4=2×4=8%

4
An inspector rejects 0.08% of the meters as defective. How many will be examine to project ?
A.    250
B.    2500
C.    25000
D.    250000

Answer : B.   2500

Explanation:
Let the number of meters to be examined be x.

Then, 0.08% of x =2

\([({8 \over 100}) \times({1\over100}) \times x] = 2\)

\(x = \bigg[{(2\times100 \times100) \over8}\bigg]\) = 2500.  

5
Sixty five percent of a number is 21 less than four fifth of that number. What is the number ?
A.    130
B.    135
C.    140
D.    145

Answer : C.  140

Explanation:
Let the number be x.

Then, \(4 \times {x \over 5}\) –(65% of x) = 21

=> \(4{x\over 5} –65 {x \over 100} = 21\)

=> 15 x = 2100

=> x = 140.
 

6
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. What are the marks obtained by them?
A.    42,33
B.    42,36
C.    44,33
D.    44,36

Answer : A.  42,33

Explanation:

Let the marks secured by them be \(x\) and \((x+9)\)

sum of their marks =\(x+(x+9)=2x+9\)
Given that \((x+9)\) was 56% of the sum of their marks.
⇒ \((x+9)={56\over100}(2x+9)\)
⇒ \((x+9)={14\over25}(2x+9)\)
⇒ \(25x+225=28x+126\)
⇒ \(3x=99\)
⇒ \(x=33\)

Then \((x+9)=33+9=42\)
Hence their marks are 33 and 42
 



7
 If A =x% of yy and B =y%  of x , then which of the following is true?
A.    None of these
B.    A is smaller than B.
C.    Relationship between A and B cannot be determined.
D.    A is greater than B.

Answer : A.  None of these

Explanation:
\(A={x\over 100} \times y={xy\over 100}.......(1)\)

\(B={y\over 100} \times x={yx\over 100}.......(2)\)

Therefore A = B

8
If 20% of a = b, then b% of 20 is the same as:
A.    None of these
B.    10% of a
C.    4% of a
D.    20% of a

Answer : C.  4% of a

Explanation:
20% of a=b

⇒ \(b={20a \over 100}={a\over5}\)

b% of 20 = \(20 \times {b\over 100}\)

\(={b\over5}={a\over5} \times {1\over 5}= {a\over 25}\)

\(={4a \over 100}=4\%\) of a