Question

Taruna borrowed twice the money borrowed by Nisha at the same rate of 10% simple interest per annum for 5 years. If Nisha paid Rs.53000 less than the interest paid by Taruna, find the money borrowed by both of them.

Answer 1

Let the borrowed money by Jaruna be Rs. x and by Nisha be Rs. y.

Rate $=10\%$,

$T=5$ years

S.I for Jaruna$=\frac{P\times R\times T}{100}$

$=\frac{x\times 10\times 5}{100}$

$=$Rs. $\frac{x}{2}$

S.I for Nisha$=\frac{y\times 10\times 5}{100}$

$=$Rs. $\frac{y}{2}$

Amount for Jaruna$=SI+x$

$=$Rs. $\frac{3x}{2}$

For Nisha$=$Rs. $\frac{3y}{2}$.

Amount paid by Nisha: $\frac{3x}{2}-\frac{3y}{2}=53000$

$3x-3y=1060000$ ……….$\left(1\right)$

$x=2y$ ………

$x-2y=0$ ………..$\left(2\right)$

$x=2y$

$=2\times 35333.3$

$x=$Rs. $70666.6$,

Multiplying equation (2)$by$(3)$

$3x-3y=106000$

$3x-6y=0$

_______________

$3y=106000$

_______________

$y=35333.3$ Rs.

Money borrowed by Jaruna $=$Rs. $70666.6$

and by Nisha $=$Rs. $35333.3$.