Question

The simple interest on a certain sum for $2.5$ years at $12$ per cent per annum is $Rs.300$ less than the simple interest on the same sum for $4.5$ years at $8$ per cent per annum. Find the sum.

Answer 1

Let Rs. P be the sum

At $12\%$ per annum the interest for $8$ years

$=\frac{P\times 12\times 8}{100}=\frac{24P}{25}$

qat $14\%$ per annum the interest for $5$ years

$=\frac{P\times 14\times 5}{100}=\frac{7P}{10}$

ACQ,

$\Rightarrow \frac{24P}{25}=3120+\frac{7P}{10}$

$\Rightarrow (\frac{24}{25}-\frac{7}{10})P=3120$

$\Rightarrow \left(\frac{96-70}{100}\right)P=3120$

$\Rightarrow \left(\frac{26}{100}\right)P=3120$

$\Rightarrow P=\frac{3120\times 100}{26}$

$\Rightarrow P=12000$