Question

Two numbers are respectively 20% and 30% less than the third number. What is the second number as a percentage of the first?
A. 87.5%
B. 88%
C. 77.5%
D. 87%

Answer 1

Hint: Let the first number be x, second number be y and third number be z. The second number as a percentage of the first number will be $ \dfrac{y}{x} \times 100 $ . x is 20% less than z and y is 30% less than z. So find x and y values in terms of z and substitute in $ \dfrac{y}{x} \times 100 $ to find the percentage.

Complete step-by-step answer:
We are given that two numbers are respectively 20% and 30% less than the third number.
We are given to find the second number as a percentage of the first.
Let the first number be x, second number be y and third number be z.
The number x is 20% less than z, this means the value of x in terms of z is
$\Rightarrow x = z - \dfrac{{20z}}{{100}} = \dfrac{{100z - 20z}}{{100}} = 0.8z $
The number y is 30% less than z, this means the value of y in terms of z is
 $\Rightarrow y = z - \dfrac{{30z}}{{100}} = \dfrac{{100z - 30z}}{{100}} = 0.7z $
The second number as a percentage of the first is $ \dfrac{y}{x} \times 100 $
Substituting the values of x and y in terms of z, we get
 $ \Rightarrow \dfrac{{0.7z}}{{0.8z}} \times 100 = \dfrac{7}{8} \times 100 = \dfrac{{700}}{8} = 87.5\% $
The second number as a percentage of the first number is $87.5$.
So, the correct answer is “Option A”.

Note: Here we have to find the second number as a percentage of the first number, so we have divided the second number by the first number. If we are asked to find the first number as a percentage of the second number, we have to divide the first number by the second number and multiply it by 100. Specifying one number as a percentage of another means specifying the fraction of the second quantity the first comprises.