If A1 is 19 times more than A2, then A2 is what percentage less than A1?

a) 85 percent
b) 105 percent
c) 100 percent
d) 95 percent

Ans : d) 95 percent

SSC Constable GD Paper : 2024 – Elementary Mathematics

Solution :

Let ( A_1 ) and ( A_2 ) represent the two quantities, where ( A_1 ) is 19 times more than ( A_2 ).
This means: A_1 = A_2 + 19A_2 = 20A_2

We need to find what percentage ( A_2 ) is less than ( A_1 ). The percentage decrease is calculated using the formula:
Percentage decrease = $ \frac{A_1 – A_2}{A_1} \times 100 $

Substitute ( A_1 = 20A_2 ) into the formula:
$ \text{Percentage decrease} = \frac{20A_2 – A_2}{20A_2} \times 100 = \frac{19A_2}{20A_2} \times 100 = \frac{19}{20} \times 100 = 95\% $

Thus, ( A_2 ) is 95% less than ( A_1 ).