A man gave 50% of his savings of ₹ 84,100 to his wife

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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

1. ₹ 20,000
2. ₹ 20,050
3. ₹ 22,000
4. ₹ 22,050

Correct Option: A

Amount given to sons = 84100 ×	1	= ₹ 42050
	2

Let Amount given to B = ₹ y
∴ Amount given to A = ₹ (42050 – y)

A = P		1 +	R		_T
			100

⇒ (42050 – y )		1 +	R		₃	= y		1 +	R		₅
			100						100

⇒ (42050 – y ) = y		1 +	R		₂
			100

⇒ (42050 – y ) = y		1 +	5		₂
			100

⇒ (42050 – y ) = y		1 +	1		₂
			20

⇒ 42050 – y = y		21		²
		20

⇒ 42050 – y =	441y
	400

⇒ 42050 =	441y	+ y
	400

⇒ 42050 =	441y + 400y
	400

⇒ 42050 =	841y
	400

⇒ 841 y = 42050 × 400

⇒ y =	42050 × 400	= ₹ 20,000
	841