Question

Divide a sum of $Rs.13500$ into two parts such that if one part be lent at $8\frac{1}{3}\%$ per annum for $2$ years $9$ months and the other at $7\frac{1}{2}\%$ per annum for $1$ year $8$ months, the total interest received in $Rs.2375$.

Answer 1

Let the one part be $x$ and other be $(13500-x)$

$\frac{x}{100}\times \frac{25}{3}\times (2+\frac{9}{12})+\left(\frac{13500-x}{100}\right)\times \frac{15}{2}\times (1+\frac{8}{12})$

$\frac{x}{12}\left(\frac{11}{4}\right)+\left(\frac{13500-x}{100}\right)\times \frac{15}{2}\times \frac{5}{}3=2375$

$5x=114000-81000$

$x=6600$

$13500-6600=6900$

So, two parts are $Rs6600$ and $Rs6900$