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 Harti 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

Given, 

C.I that Kamla receive = Rs.210 

S.I that Kamla paid = Rs.200 

Time = 2 years 

So,

S.I \(=\frac{P \times R \times T}{100}\) \(=\frac{(P \times R \times 2)}{100}\) = 200

\({P}\times{R}\) = 10000 ................(i)Also,

C.I. = Total amount - Principal amount

C.I \(={P}({1}+\frac{R}{10})^T-{P}\)

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

we know, (a + b)² = a² + b² + 2ab

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

\(210= p({1}+\frac{R^2}{10000}+\frac{R}{50}-p\)

\(210=p({1}+\frac{R}{10000}+\frac{R}{50})-1\)

\(210= p(\frac{R^2}{10000}+\frac{R}{50})\)

\(210 =\frac{PR^2}{10000}+\frac{PR}{50}\)

from {i}, we have PR = 10000

∴ 210 \(=\frac{10000R}{10000}+\frac{10000}{50}\)

210 = R+ 200

R = 10% 

From equation (i)

\({P\times R}\) = 10000

 \({P\times R}\) = 10000P \(=\frac{10000}{10}\) = Rs. 1000