Tick ( ) the correct answer in the following: If the compound interest on a sum for 2 years at 121 2 % per annum is Rs. 510, the simple interest on the same sum at the same rate for the same period of time is.

Tick ( ) the correct answer in the following: If the compound int…

MCQ

Tick $(\checkmark)$ the correct answer in the following: If the compound interest on a sum for $2$ years at $12\frac{1}{2}\%$ per annum is $Rs. 510,$ the simple interest on the same sum at the same rate for the same period of time is.

A
$Rs. 400$
B
$Rs. 450$
C
$Rs. 460$
✓
$Rs. 480$

✓

Answer

Correct option: D.

$Rs. 480$

$C.I$ on a sum $= Rs. 510$
Rate $(R) 12\frac{1}{2}\%=\frac{25}{2}\%\text{ p.a}$
Period $(n) = 2$ years
$\text{C.I} = \text{A} - \text{P}=\text{P}\Big(1+\frac{\text{R}}{100}\Big)^{\text{n}}-\text{P}$
$\text{C.I}=\text{P}\Bigg[\Big(1+\frac{\text{R}}{100}\Big)^{\text{n}}-1\Bigg]$
$\Rightarrow510=\text{P}\Bigg[\Big(1+\frac{\text{R}}{2\times100}\Big)^2-1\Bigg]$
$\Rightarrow510=\text{P}\Big[\frac{9}{8}\times\frac{9}{8}-1\Big]$
$\Rightarrow510=\text{P}\Big[\frac{81}{64}-1\Big]$
$\Rightarrow510=\text{P}\Big(\frac{17}{64}\Big)=\text{P}=\frac{510\times64}{17}$
$\text{P}=\text{Rs. }1920$
$\therefore\text{S.I}=\frac{\text{PRT}}{100}=\frac{1920\times25\times2}{100\times2}$
$=\text{Rs. }480$

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