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- Standard 13
- Quantitative Aptitude
A man gave $50 \%$ of his savings of ₹ $84,100$ 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 $18$ years, would receive the same amount at $5 \%$ compound interest per annum. The share of $B$ was (In ₹)
$20000$
$20050$
$22000$
$22050$
Solution
(a) Total savings $=₹ 84100$
Share of wife $=50 \%(84100)=42050$
Let the share of $B$ be $^{\circ} b^{\prime}$
Share of $A=42050-b$
For $A,$ time $=5$ years
Rate $=5 \%$
Amount $=P \times\left[1+\frac{r}{100}\right]^{n}$
$=(42050- b )\left[1+\frac{5}{100}\right]^{5}$
$=(42050-b) \times 1.27$
For $B ,$ time $=7$ years
Amount $=b\left[1+\frac{5}{100}\right]^{7}$
$=1.4 b$
Given, amount of $A=$ amount of $B$
$(42050-b) \times 1.27=1.4 b$
$53403-1.27 b=1.4 b$
$b=20,000$
Hence, $B$ got $₹ 20,000$
