A sum of Rs. 1550 was lent partly at 5% and partly at 8% pa simple interest. The total interest received after 5 yr was Rs. 500. Find the ratio of the

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A sum of Rs. 1550 was lent partly at 5% and partly at 8% pa simple interest. The total interest received after 5 yr was Rs. 500. Find the ratio of the money lent at 5% to that at 8%?
1. 12 : 17
2. 17 : 12
3. 19 : 12
4. 16 : 15

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Correct Answer - Option 4 : 16 : 15

Given:

Sum = Rs. 1550

Rate = 5% and 8%

Time = 5 yrs

SI = Rs. 500

Formula Used:

S.I = P × r × t/100

Calculations:

Let the sum lent at 5% be P

Sum lent at 8% = (1550 - P)

Then, (P × 5 × 5)/100 + [(1550 - P) × 8 × 5] /100 = 500

⇒ 25P – 40P + 1550 × 40 = 50000

⇒ -15P + 62000 = 50000

⇒ -15P = 50000 – 62000

⇒ -15P = -12000

⇒ P = 800

Sum lent at 8% = 1550 – 800 = 750

required ratio = 800 : 750 = 16 : 15.

∴ The ratio of money lent at 5% to that at 8% is 16 : 15.