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.