Question

Question 131

Divide ₹ 10000 in two parts, so that the simple interest on the first part for 4 yr at 12% per annum may be equal to the simple interest on the second part for 4.5 yr at 16% per annum.

Answer 1

Given, we have divide ₹ 10000 in two parts such that SI on first part for 4 yr at 12% per annum may be equal to the SI on second part for 4.5 yr at 16%.

Let first part = ₹ x
Then, second part = ₹( 10000 - x)
For first part, we have
$P_1$= ₹ x
$T_1=4yrand{R}_1=12$

For second part (10000 - x), we have,
$P_2$ = ₹ (10000 - x),
$T_2=4.5yrand{R}_2=16\%$
$\therefore S{I}_2=\frac{P_2\times R_2\times T_2}{100}=\frac{(10000-x)\times 16\times 4.5}{100}$

Since, $S{I}_1$ is equal to $S{I}_2$.

Then, according to the question,

$\frac{x\times 12\times 4}{100}=\frac{(10000-x)\times 16\times 4.5}{100}\Rightarrow 48x=(10000-x)\times 16\times 4.5\Rightarrow \frac{48x}{4.5\times 16}=(10000-x)\Rightarrow \frac{48x\times 10}{45\times 16}=10000-x\Rightarrow \frac{2}{3}x=10000-x\Rightarrow \frac{2}{3}x+x=10000\Rightarrow \frac{5x}{3}=10000\Rightarrow x=10000\times \frac{3}{5}=6000$
First part = x = ₹ 6000
Second part = 10000 - x = 10000 - 6000 = ₹ 4000
Hence, two parts of the sum are ₹ 6000 and ₹4000.