Question

Divide Rs. 1301 between A and B, so that the amount of A after 7 years is equal to the amount of B after 9 years, the interest being compounded at$4\%$ per annum.

• A. Rs. 576 and Rs. 685
• B. Rs. 676 and Rs. 625
• C. Rs. 676 and Rs. 645
• D. Rs. 642 and Rs. 625

Answer 1

The correct option is B

Rs. 676 and Rs. 625

Let the two parts be $Rs.xandRs.(1301-x)$.

$\Rightarrow$$x{(1+\frac{4}{100})}^7=(1301-x){(1+\frac{4}{100})}^9$

$\Rightarrow$ $\frac{x}{(1301-x)}={(1+\frac{4}{100})}^2$

$\Rightarrow$ $\frac{x}{(1301-x)}=(\frac{26}{25}\times \frac{26}{25})$

$\Rightarrow$ $625x=676(1301-x)$

$\Rightarrow$ $1301x=676\times 1301$

$\Rightarrow$ x = 676

So, the two parts are Rs. 676 and Rs. (1301 - 676) i.e. Rs. 676 and Rs. 625