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

Total savings = Rs. 84100
Share of wife = $$\frac{50}{100}\times 84100 = 42050$$
Let the share of B be 'b'
Share of A = 42050 - b
For A, time = 5 years
Rate = 5%
Amount = $$P \times [1 + \frac{r}{100}]^n$$
Amount = $$(42050 - b)[1 + \frac{5}{100}]^5$$
Amount = $$(42050 - b) \times 1.27$$
For B, time = 7 years
Amount = $$b[1 + \frac{5}{100}]^7$$
Amount = $$1.4 b$$

Given that,
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 Rs. 20,000