Question

A certain sum of money lent out at $6\frac{2}{3}\%$ p.a. produces the same simple interest in $6$ years as $Rs3200$ lent out at $8\frac{2}{5}\%$p.a. for $7$ years. Find the sum.

Answer 1

We have,

Principal value $P=3200$

Rate $=R=8\frac{2}{5}$

Time $=T=7year$

Then using

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

$=\frac{3200\times \frac{42}{5}\times 7}{100}$

$=\frac{3200\times 42\times 7}{5\times 100}$

$=\frac{32\times 42\times 7}{5}$

$S.I.=Rs1881.6$

In the second case

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

$1881.6=\frac{P\times \frac{20}{3}\times 7}{100}$

$1881.6\times 100=P\times \frac{20}{3}\times 7$

$P=\frac{1881.6\times 100\times 3}{20\times 7}$

$P=\frac{1881.6\times 5\times 3}{7}$

$P=Rs4704$

Hence, this is the answer.