Question

In $4$ years, $Rs.6500$ amounts to $Rs.8840$ at a certain rate of interest. In what time will $Rs.1600$ amount to $Rs.1816$ at the same rate?

Answer 1

Given that,

Time $\left(T\right)=4$ years

principle $\left(P\right)=Rs.6500$

Amount $\left(A\right)=Rs.8840$

Interest $(S.I)=8840-6500=Rs.2340$

We know that,

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

$\Rightarrow 2340=\frac{6500\times r\times 4}{100}$

$\Rightarrow R=\frac{2340\times 100}{6500\times 4}$

$\Rightarrow R=9$

then,

$P_1=Rs.1600$

$A_1=Rs.1816$

$S.I_1=Rs.1816-Rs1600=Rs.216$

$S.I_1=\frac{P_1\times R\times T_1}{100}$

$\Rightarrow 216=\frac{1600\times 9\times t}{100}$

$\Rightarrow T_1=\frac{216\times 100}{1600\times 9}$

$\Rightarrow T_1=\frac{3}{2}$

Therefore, $T_1=1\frac{1}{2}$ years.