# percentage

6.

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

Explanation:

20% of a = b          20     a = b.
100

b% of 20 =         b     x 20         =         20     a x     1     x 20         =     4     a = 4% of a.
100     100     100     100

7.

In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is of the number of students of 8 years of age which is 48. What is the total number of students in the school?

A.     72    B.     80
C.     120    D.     150
E.     100

Explanation:

Let the number of students be x. Then,

Number of students above 8 years of age = (100 – 20)% of x = 80% of x.

80% of x = 48 +     2     of 48
3

80     x = 80
100

x = 100.

8.

Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
A.     2 : 3    B.     1 : 1
C.     3 : 4    D.     4 : 3

Explanation:

5% of A + 4% of B =     2      (6% of A + 8% of B)
3

5      A +     4      B     =     2         6      A +     8      B
100     100     3     100     100

1      A +     1      B     =     1      A +     4      B
20     25     25     75

1     –     1      A =          4     –     1      B
20     25     75     25

1      A =     1      B
100     75

A     =     100     =     4     .
B     75     3

Required ratio = 4 : 3

9.

A student multiplied a number by     3     instead of     5     .
5     3

What is the percentage error in the calculation?

A.     34%    B.     44%
C.     54%    D.     64%

Explanation:

Let the number be x.

Then, error =     5     x –     3     x =     16     x.
3     5     15

Error% =         16x     x     3     x 100     % = 64%.
15     5x

10.

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