A sum of ₹ 10,000 is lent partly at 8% and remaining

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A sum of ₹ 10,000 is lent partly at 8% and remaining at 10% per annum. If the yearly interest on the average is 9.2%, the two parts are :

1. ₹ 4000, ₹ 6000
2. ₹ 4500, ₹ 5500
3. ₹ 5000, ₹ 5000
4. ₹ 5500, ₹ 4500

Correct Option: A

Let p be lent at 8%, then (10000 – p) is lent at 10%.
According to question ,

∴	10000 × 9.2 × t	=	p × 8 × t	+	(10000 - p) × 10 × t
	100		100		100

⇒	920000	=	8pt	+	(10000 - p)10t
	100		100		100

⇒ 92000t = 8pt + (10000 – p) 10t
⇒ 92000t = 8pt + (10000 – p) 10t
⇒ 92000 = 8p + 100000 – 10p
⇒ 2p = 8000
⇒ p = 4000
∴ First part = ₹ 4000
Second part = 10000 - 4000 = ₹ 6000