Question

A: Calculate the difference between the simple interest and the compound interest on Rs. $4,000$ in $2$ years at $8\%$ per annum compounded yearly.
B: On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simpled interest for a year is Rs. $180$/-. Find the sum lent out, if the rate of interest in both the cases is $10\%$ per annum. Then, find $10A+B$.

• A. $72256$
• B. $720256$
• C. $722056$
• D. $722506$

Answer 1

The correct option is A $72256$

Part $A$ :

$\Rightarrow$ $S.I.=\frac{P\times R\times T}{100}=\frac{4000\times 8\times 2}{100}$

$\therefore$ $S.I.=Rs.640$

$\Rightarrow$ $C.I.=P(1+\frac{R}{100}{)}^T-P=8000\times (1+\frac{8}{100}{)}^2-8000$

$\Rightarrow$ $C.I.=8000\times \frac{27}{25}\times \frac{27}{25}-8000$

$\therefore$ $C.I.=Rs.665.6$

$\Rightarrow$ Difference between C.I. and S.I. = $Rs.665.6-Rs.640=Rs.25.6$

$\therefore$ $A=25.6$

$\Rightarrow$ Part $B$ :

$\Rightarrow$ Here, $R=10\%$ and $C.I.-S.I.=Rs.180$

$\Rightarrow$ $S.I.=\frac{P\times R\times T}{100}=\frac{10\times P\times 1}{100}$

$\therefore$ $S.I.=\frac{P}{10}$

$\Rightarrow$ $C.I.=P(1+\frac{R}{200}{)}^2-P$

$\Rightarrow$ $C.I.=P\times (\frac{210}{200}{)}^2-P$

$\Rightarrow$ $C.I.=\frac{441P}{400}-P$

$\therefore$ $C.I.=\frac{41P}{400}$

$\Rightarrow$ $C.I.-S.I.=\frac{41P}{400}-\frac{P}{10}=\frac{P}{400}$

$\Rightarrow$ Given difference is $180$

$\therefore$ $\frac{P}{400}=180$

$\therefore$ $P=Rs.72000$

$\therefore$ $B=72000$

$\Rightarrow$ $10A+B=10\times 25.6+72000=72256$