Question

Mohan lends Rs. 4800 to John for $4\frac{1}{2}$ years and Rs. 2500 to Shyam for 6 years and receives a total sum of Rs. 2196 as interest. Find the rate percent per annum, it being the same in both the cases.

Answer 1

In the first case:
P=Rs. 4800
R=x% (suppose)
T= $4\frac{1}{2}years=\frac{9}{2}years$
Interest= $\frac{P\times T\times R}{100}$
$=Rs.\frac{4800\times x\times 9}{100\times 2}=Rs.24\times x\times 9=Rs.216x$
In the second case:
P= Rs. 2500
R=x%
T=6 years
Interest= $\frac{P\times T\times R}{100}$
$=Rs.\frac{2500\times x\times 6}{100}=Rs.25\times x\times 6$
=Rs. 150x
According to statement,
Interest in first case + Interest in second case= Rs. 2196
$\therefore$ Rs. 216x+Rs. 150x =Rs. 2196
$\Rightarrow Rs.366x=Rs.2196$
$\Rightarrow x=\frac{2196}{366}$
$\Rightarrow x=6$
$\therefore$ Rate=6%