Question

The simple interest on a certain sum compoudes to Rs. $256$ in $2$ years, whereas the compund interest on the same sum at the same rate and for the same time computes to Rs. $276.48$. Find the rate per cent and the sum.

• A. $18\%,Rs.800$
• B. $16\%,Rs.800$
• C. $14\%,Rs.800$
• D. $12\%,Rs.800$

Answer 1

The correct option is B $16\%,Rs.800$

let the sum is P and rate of interest r% per annum

Time=2 years

Simple interest=Rs.256

Compound interest=Rs.276.48

Difference between C.I and S.I$=276.48-256=Rs.20.48$

simple interest$=\frac{PRT}{100}$

$\Rightarrow \frac{P\times R\times 2}{100}=256$

$\Rightarrow \frac{PR}{100}=128$........eq1

Difference between compound interest and simple interest is the interest calculated on the interest of the first year$=\frac{PR\times 1}{100}=\frac{PR}{100}$

$\Rightarrow \frac{\frac{PR}{100}\times R\times 1}{100}=20.48$

$\Rightarrow \frac{P(R{)}^2}{10000}=20.48$.....eq2

Dividing eq2 by eq1

$\Rightarrow \frac{P(R{)}^2}{10000}\times \frac{PR}{100}=\frac{20.48}{128}$

$\Rightarrow \frac{R}{100}=\frac{20.48}{128}$

$\Rightarrow R=\frac{20.48\times 100}{128}=16$%

Put the value of R in eq 1

$\Rightarrow \frac{P16}{100}=128$

$P=\frac{128\times 100}{16}=Rs.800$