Question

A man gave $50$% of his savings of $1,68,200$ to his wife and divided the remaining sum among his two sons A and B of $15$ and $13$ years of age respectively. He divided it in such a way that each of his sons, when they attain the age of $20$ years would receive the same amount at $5$% compound interest per annum, the share of B was -

• A. $20000$
• B. $30000$
• C. $40000$
• D. $50000$

Answer 1

The correct option is C $40000$

$P=\frac{1}{2}\times 168200=Rs.84100$

Let's show of $B$ be $x=$show of $A=(P-x)$

Amount received by $A$ on age $20$

$A_1=P(1+\frac{r}{100}{)}^n=$$(P-x)(1+\frac{5}{100}{)}^5$

Amount received by $B$ on age $20$

$A_2=P(1+\frac{r}{100}{)}^n=$$\left(x\right)(1+\frac{5}{100}{)}^7$

Given that $A_1=A_2$

$⟹(p-x)(1.05{)}^5=x(1.05{)}^7$

On solving we get, $x=40,000$