Question

If the compound interest on a certain sum $at16\frac{2}{3}\%\text{for 3 years is Rs. 1270, the simple}$ interest on the same at the same rate and for the same period is:

• A. Rs. 1200
• B. Rs. 1165
• C. Rs. 1080
• D. Rs. 1220

Answer 1

The correct option is C Rs. 1080

$\begin{array}{cc}& \text{Let the sum be Rs.}x\text{Then,}\\ C.I& =[x\times {(1+\frac{50}{3\times 100})}^3]-x\\ & =(\frac{343x}{216}-x)=\frac{127x}{216}\\ \therefore \frac{127x}{216}& =1270\\ orx& =\frac{1270\times 216}{127}=2160.\\ & \text{Thus, the sum is Rs. 2160.}\\ \therefore S.I.& =Rs.(2160\times \frac{50}{3}\times 3\times \frac{1}{100})\\ & =Rs.1080.\end{array}$