A sum of Rs. 7,930 is divided into three parts and given

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A sum of Rs. 7,930 is divided into three parts and given on loan at 5% simple interest to A, B and C for 2, 3 and 4 years respectively. If the amounts of all three are equal after their respective periods of loan, then A received a loanof

1. Rs. 3,050
2. Rs. 2,760
3. Rs. 2,750
4. Rs. 2,800

Correct Option: B

Let the loans taken by A, B and C be Rs. p, Rs. q and Rs. r respectively.
∴ p + q + r = Rs. 7930
We can find the required answer with the help of given formula ,

S.I =	Principal × Time × Rate
	100

According to the question,

p +	p × 2 × 5	= q +	q × 3 × 5	= r +	r × 4 × 5
	100		100		100

⇒	100p + 10p	=	100q + 15q	=	100r + 20r
	100		100		100

⇒ 110p = 115q = 120r
⇒ 22p = 23q = 24r

⇒	22p	=	23q	=	24r
	6072		6072		6072

[LCM of 22, 23 and 24 = 6072]

⇒	p	=	q	=	r
	276		264		253

∴ p : q : r = 276 : 264 : 253
Sum of terms of ratio = 276 + 264 + 253 = 793

∴ A’s loan =	276	× 7930 = Rs. 2760
	793