Question

P and Q invest $₹36,000$ and $₹25,000$ respectively at the same rate of interest per year. If at the end of 4 years P get $₹3,080$ more interest than Q, find the rate of interest.

Answer 1

Step 1: Calculate the simple interest for P
Let rate of interest be R% p.a.
Given:
T = 4 years
Principal amount for $P=₹36,000$
$\therefore S.I\text{for}P=\frac{P\times R\times T}{100}$
$=\frac{36000\times R\times 4}{100}$
$=\left(1440\right)\times R...\left(i\right)$

Step 2 : Calculate the simple interest for Q
Principal amount for $Q=₹25,000$
T = 4 years
$\therefore S.I\text{for}Q=\frac{P\times R\times T}{100}$
$=\frac{25000\times R\times 4}{100}$
$=1000R...\left(ii\right)$

Step 3: Calculate the rate of interest
Now, according to the question:
S.I for P = S.I for Q + $₹3080$
$\Rightarrow 1440R-1000R=₹3080$
$\Rightarrow 440R=3080$
$\therefore R=7\text{\% p.a.}$
Hence, the rate of interest is 7% p.a.