Question

Kamala borrowed from Ratan a certain sum at a certain rate for two years simple interest. She lent this sum at the same rate to Hari for two years compound interest. At the end of two years, she received Rs$210$ as compound interest but paid Rs$200$ only as simple interest. Find the sum and the rate of interest.

Answer 1

Let the sum be Rs. P and the rate of intersect be R%

We know that Kamala paid Rs. 200 as simple interest

$\therefore 200=\frac{PR\times 2}{100}$

PR=10000 _______ (1)

Also, Kamala received Rs 210 as compound interest

$\therefore 210=P(1+\frac{R}{100}{)}^2-1$

$210\left(1000\right)=P(R^2+200R)$

$210R=R^2+200R$ from (1)

$\Rightarrow R^2-210R+200R=0$

$\Rightarrow R^2-10R=0$

$\Rightarrow R(R-10)=0$ $\therefore R\ne 0,R=10$%

put R=10 in (1) $P\times 10=10,000$

$\therefore P=Rs.1000$

Thus, the required sum is Rs 1000 and rate of interest is 10%