4 Mark Question

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.

Vidyadip · Accepted Answer

Let the sum be Rs. P and the rate of interest be R%.
We know that Kamla paid Rs. 200 as simple interest.
$\therefore\ 200=\frac{\text{PR(2)}}{100}$
$\text{PR}=10,000...(1)$
Also, Kamla received Rs. 210 as compound interest.
$\therefore\ 210=\text{P}\Big(1+\frac{\text{R}}{100}\Big)^{2}-1$
$210(10,000)=\text{P}(\text{R}^{2}+200\text{R})$
$210\text{ R}=\text{ R}^{2}+200\text{R}$ [from (1)]
R = 10% p.a.
Putting the equation in (1), we get:
P = 1,000
Thus, the required sum is Rs. 1,000 and the rate of interest is 10%.

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