Question

A sum of money at simple interest amount to Rs. $9440$ in $3$ years. if the rate of interest is increased by $25\%$ the same sum amounts to Rs $9800$ in the same time . The original rate of interest is

• A. $10\%$ p.a
• B. $8\%$ p.a
• C. $7.5\%$ p.a
• D. $6\%$ p.a

Answer 1

The correct option is D $6\%$ p.a

We take the principal $=P$, rate $=R$, time $=T$.

So, amount $A=P+I=P+$ $\frac{PRT}{100}.$

In the first situation, we have

$A=$ Rs. $9440,T=3$ yr. $P=P,R=R\%$.

$\therefore P+\frac{PR\times 3}{100}=9440\Rightarrow 100P+3PR=944000$ ........(i)

In the second situation, we have

$A=$ Rs. $9800,T=3$ yr. $P=P,R=($ $R+R\times \frac{25}{100}=\frac{5R}{4}$ $)\%$

$\therefore P+\frac{3PR}{100}\times \frac{5}{4}=9800\Rightarrow 80P+3PR=784000$ ........(ii)

Now, $\left(i\right)-\left(ii\right)$

$\Rightarrow 20P=160000$

$\Rightarrow P=$ Rs. $8000.$

Then, in the first situation,

$\therefore P+\frac{3PR}{100}=9440\Rightarrow 8000+\frac{3\times 8000\times r}{100}=9440\Rightarrow 240R=1440\Rightarrow R=6$

So, the required rate is $6\%$.