A sum of 1550 was lent partly at 5% and partly at 8% simple

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A sum of 1550 was lent partly at 5% and partly at 8% simple interest. The total interest received after 3 years is 300. The ratio of money lent at 5% to that at 8% is :

1. 5 : 8
2. 8 : 5
3. 31 : 6
4. 16 : 15

Correct Option: D

Let the sum lent at the rate of interest 5% per annum is p and at the rate of interest 8% per annum is (1550 – p)
According to the question,

p × 5 × 3	+	(1500 - p) × 8 × 3	= 300
100		100

⇒	15p	+	37200 - 24p	= 300
	100		100

⇒ 15p + 37200 – 24p = 300 × 100
⇒ 9p = ₹ 7200
∴ p = 800 and, 1550 – p = 1550 – 800 = ₹ 750
∴ Ratio of money lent at 5% to that at 8% = 800 : 750 = 16 : 15