## Q1: If 12% of x is equal to 6% of y, then 18% of x will be equal to how much percent of y?

Solution:

12% of x = 6% of y

x(12%) = y(6%)

Let 18% of x = a% of y

x(18%) = y(a%)

x(12%) = y(6%)

x(18%) = y(a%)

Cross multiply

x(12%) X y(a%) = x(18%) X y(6%)

12axy = 108xy

12a = 108

Dividing both sides by the coefficient of “a”

a = 108/12

a = 9%

## Q2: If a number is 20% more than the other, how much percent is the second number less than the first?

Solution:

Let the smaller number be 100

The bigger number is 20% more, that is [100 + (20% of 100)]

= (100 + 20) = 120

Now, the percentage which 20 is from 120

= (20/120) X 100 = 16.67%

## Q3: If A’s income is 25% less than that of B, then how much percent is B’s income more than that of A?

Solution:

Let’s assume that B makes #100

A makes 25% less than B

= [100 – (25% of 100)]

= [100 – (25)] = #75

Now, the question becomes 100 is what percent is 75?

This can be solved by putting them up in proportion

“A” makes 75

“B” makes 100

Let percentage of “B” = y

Percentage of “A” = 100

So;

75 = 100

100 = y

Cross multiply

75 x y = 100 x 100

75y = 10000

Dividing both sides by the coefficient of y.

y = (10000)/75 = 133.3%

Therefore, B’s income is (133.3 – 100)% more than A’s income

B’s income = 33.3% more

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## Q4: If the given two numbers are respectively 7% and 28% of a third number, then what percentage is the first of the second?

Solution:

Let the 3rd number be y

First number = 7y/100

Second number = 28y/100

So, percentage of the first in the second

= [(7y/100) Ă· (28y/100)] x 100

= [(7y/100) x (100/28y)] x 100

= 7/28 x 100

= 1/4 x 100 = 25%

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