Divide ₹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.
Answer
Answer (as printed):
Explanation
Let the two parts be ₹x and ₹(1301−x). $x\left(1+\frac{4}{100}\right)^{7}=(1301-x)\left(1+\frac{4}{100}\right)^{9}$ $\Leftrightarrow \frac{x}{(1301-x)}=\left(1+\frac{4}{100}\right)^{2}=\left(\frac{26}{25} \times \frac{26}{25}\right)$ $\Leftrightarrow 625x=676(1301-x)$ $\Leftrightarrow 1301x=676 \times 1301 \Leftrightarrow x=676$. So, the two parts are ₹676 and ₹(1301−676) i.e. ₹676 and ₹625.
Explanation as extracted from the printed page; notation may be imperfect.