A sum of Rs. 2800 is divided into two parts in such a way

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A sum of Rs. 2800 is divided into two parts in such a way that the interest on both the parts is equal. If the first part is lent at 9% p.a. for 5 years and second part is for 6 years at 10% p.a., find the two sums.

1. Rs. 1800, Rs. 1000
2. Rs. 1600, Rs. 1200
3. Rs. 1400, Rs. 1400
4. Rs. 1300, Rs. 1500

Let first part be y.
∴ Second part = Rs. (2800 – y)
According to the question,

SI =	Principal × Time × Rate
	100

∴	y × 5 × 9	=	(2800 - y) × 6 × 10
	100		100

⇒ 3y = 4 × 2800 – 4y
⇒ 7y = 4 × 2800

⇒ y =	4 × 2800	= Rs. 1600
	7

∴ Second part = Rs. (2800 – 1600) = Rs. 1200