Arun borrowed a certa

Question

Arun borrowed a certain sum from Manish at a certain rate of simple interest for 2 years. He lent this sum to Sunil at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 2400 as compound interest but paid Rs. 2000 only as simple interest. Find the rate of interest.

Options:

A . 40%

B . 30%

C . 20%

D . 10%

Answer: Option A

Answer : Option A

Explanation :

Let the sum be x
Simple interest on x for 2 years = Rs.2000
$MF#%\text{Simple interest = }\dfrac{\text{PRT}}{100}\\\\ 2000 = \dfrac{x \times \text{R} \times 2}{100}\\\\ \Rightarrow x\text{R} = 100000 \quad \color{#F00}{\text{--- (1)}}$MF#%
Compound Interest on x for 2 years = 2400
$MF#%\text{P}\left(1 + \dfrac{\text{R}}{100}\right)^\text{T} - \text{P} = 2400\\\\ x\left(1 + \dfrac{\text{R}}{100}\right)^2 - x = 2400\\\\ x\left(1 + \dfrac{\text{2R}}{100} + \dfrac{\text{R}^2}{10000}\right) - x = 2400\\\\ x\left(\dfrac{\text{2R}}{100} + \dfrac{\text{R}^2}{10000}\right) = 2400\\\\ \dfrac{2x\text{R}}{100} + \dfrac{x\text{R}^2}{10000} = 2400 \quad \color{#F00}{\text{--- (2)}}\\\\$MF#%
Substituting the value of xR from (1) in (2) ,we get
$MF#%\dfrac{2 \times 100000}{100} + \dfrac{100000 \times \text{R}}{10000} = 2400\\\\ 2000 + 10 \text{R} = 2400\\\\ 10 \text{R} = 400\\\\ \text{R} = 40\%$MF#%

Was this answer helpful ?

Next Question