Question

The simple and compound interests on a certain sum of money are Rs. $400$ and Rs. $420$ in $2$ years. Calculate the rate of interest.

Answer 1

$SI=\frac{PRT}{100}$

Hence,

$400=\frac{PR2}{100}$

$⟹PR=20000⟹P=\frac{20000}{R}$

Also,

$CI=P\left[\right(1+\frac{R}{100}{)}^2-1]$

$420=\frac{20000}{R}\left[\right(1+\frac{R}{100}{)}^2-1]$

Solving this we get $R=10\%$

$ALTERNATE:-$

CI for $2$ years is$=420$ Rs.

SI for $2$ years is$=400$ Rs.

Difference of CI and SI is $420-400=20$ Rs.

If $2$ years SI is $400$ Rs.,then $1$ year SI is $=\frac{400}{2}=200$

$20$ is the what percent of $200$.

$=20\times \left(\frac{100}{200}\right)=10\%$

If $510\%$ is $200$ Rs. then $100\%$ of that principal.

$=200\times \frac{100}{10}$

$=2000$

So the principal is $2000$ Rs.

Hence,

$R=\frac{SI\times 100}{PT}=\frac{400\times 100}{2000\times 2}=10\%$