If A, B, and C are three amounts of money such that B is…

If A, B, and C are three amounts of money such that B is the simple interest on A, and C is the simple interest on B, all for the same time and at the same rate of interest, then which of the following is true?

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. B² = AC.

Simple Interest = (P × R × T)/100

$C = \frac{B \times R \times T}{100}$ ⇒ $B = \frac{100C}{RT}$

$B = \frac{A \times R \times T}{100}$

⇒ $A = \frac{100B}{RT}= \frac{100}{RT} \times \frac{100C}{RT} = \frac{100^2 C}{(RT)^2}$

$B^2 = \left( \frac{100C}{RT} \right)^2 = \frac{100^2 C^2}{(RT)^2}$

$A \times C = \frac{100^2 C}{(RT)^2} \times C = \frac{100^2 C^2}{(RT)^2}$

So, B² = A × C

SSC CGL 2025 PYQ — Question 68