CAT 2025 Slot 1 QA Question 13: At a certain simple rate of interest, a given sum amounts to Rs 13920 in 3 years, and to Rs 18960 in 6 years and 6 months. If the same given sum had been invested for 2 years at the same rate as befor

Question

At a certain simple rate of interest, a given sum amounts to Rs 13920 in 3 years, and to Rs 18960 in 6 years and 6 months. If the same given sum had been invested for 2 years at the same rate as befor

Accepted Answer

Under simple interest, the increase in amount is proportional to time.
Difference in amounts = $18960 - 13920 = 5040$
Time difference = $6.5 - 3 = 3.5$ years
Annual simple interest = $\dfrac{5040}{3.5} = 1440$

Principal = $13920 - 3 	imes 1440 = 9600$
Rate = $\dfrac{1440}{9600} 	imes 100 = 15\%$