Question

A sum of money lent at simple interest amount to INR $3224$ in $2$ years and INR $4160$ in $5$ years . Find the sum and the rate of interest.

Answer 1

Amount in $5$ years = (principal $SI$ for $5$ years) =$Rs4160$.
Amount in $2$ years = (principal $SI$ for $2$ years) = $3224$.
On subtracting we get :
SI for $3$ years = $Rs(4160-3224)$ = $Rs936$.

Or $SI$ for $2$ years = $Rs\left(936x2/3\right)$ = $Rs624.$

Or sum = (amount for $2$ years) - (SI for $2$ years) = $Rs(3224-624)$ = $Rs2600.$

Now, principal = $2600,$ $SI=Rs624,$ $time=2years.$

Therefore, rate =$\left(100xSI\right)/\left(PxT\right)$= $\left(100x624\right)/\left(2600x2\right)$ =$12$