# Marshall lent certain amount of money at 10% p.a. simple interest. After a year, Rs. 5500 is repaid and the rest of the amount is repaid at 20% p.a..

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Marshall lent certain amount of money at 10% p.a. simple interest. After a year, Rs. 5500 is repaid and the rest of the amount is repaid at 20% p.a.. If the second year's interest is 11/9 of the 1st year's interest, find how much amount of money lent out initially ?
1. Rs. 11250
2. Rs. 10150
3. Rs. 11150
4. None of these

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Correct Answer - Option 1 : Rs. 11250

Given∶

Certain amount was lent a 10% p.a. simple interest.

After 1 year, Rs. 5500 is repaid and the rest of the amount is repaid at 20% p.a..

2nd year's interest is 11/9 of the 1st year's interest.

Formula Used∶

S.I. = PRT/100

A = P + S.I.

Calculation∶

Let the amount be x

S.I. = (x × 10 × 1)/100 = x/10

A = x + x/10

After 1 year, the amount becomes 1.1x out of which 5500 is repaid.

Interest for 2nd year = 20% of (1.1x - 5500)

(1.1x - 5500)/5 = 11/9 (1.1x - x)

⇒ 9.9x - 49500 = 60.5x - 55x

⇒ 4.4x= 49500

⇒ x = 11250

∴ Initially he lent out Rs. 11,250.