Question

The simple interest on a certain sum for 3 years at 8% per annum is Rs. 96 more than the simple interest on the same sum for 2 years at 9% per annum. Find the sum.

Answer 1

Let $P$ be the principal sum.

As we know that,

$S.I.=\frac{P\times r\times t}{100}$

Whereas,

$S.I.=$ Simple interest

$P=$ Principal sum

$r=$ Rate

$t=$ times

Therefore,

Condition I:- For $3$ years at the rate of $8\%$ per annum.

$S.I.=\frac{P\times 8\times 3}{100}.....\left(1\right)$

condition II:- For $2$ years at the rate of $9\%$ per annum.

$S.I.=\frac{P\times 9\times 2}{100}.....\left(2\right)$

Now according to the question-

$\frac{P\times 8\times 3}{100}=\frac{P\times 9\times 2}{100}+96$

$\Rightarrow \frac{P\times 24}{100}=\frac{(P\times 18)+9600}{100}$

$\Rightarrow 24P=18P=9600$

$\Rightarrow 24P-18P=9600$

$\Rightarrow P=\frac{9600}{6}=1600$

Hence the sum is $Rs.1600$.

Hence the correct answer is $1600$.