Mark ( ) against the correct answer in the following: At simple i… - Vidyadip

MCQ

Mark $(\checkmark)$ against the correct answer in the following:
At simple interest a sum becomes $\frac{49}{40}$ of it self in $\frac12$ years. The rate of interest per annum is:

A
$7\%$
B
$8\%$
✓
$9\%$
D
$12\%$

✓

Answer

Correct option: C.

$9\%$

Let the sum be $Rs.x$
$\text{A}=\frac{49\text{x}}{40}$
We know:
$A = P + S.I.$
$S.I. = A - P$
$=\Big(\frac{\text{49x}}{40}-\text{x}\Big)$
$=\frac{49\text{x}-40\text{x}}{40}$
$=\frac{9\text{x}}{40}$
Let the rate be $R\%$ per annum.
$\text{S.I.}=\frac{\text{P}\times\text{R}\times\text{T}}{100}$
$\Rightarrow\frac{9\text{x}}{40}=\frac{\text{x}\times\text{R}\times5}{100\times2}$
$\Rightarrow\text{R}=\frac{9\times20\times2}{10}$
$\Rightarrow\text{R}=9$

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