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### Question

A sum of Rs. 1100 is lent in two parts. One at 13% p.a. and one at 6% p.a. What is the amount lent at 13% if the total simple interest at the end of 5 years is Rs. 715?

**A**

Rs. 1100.

**B**

Rs. 1200.

**C**

Rs. 1000.

**D**

Rs. 1300.

**Soln.**

**Ans: a**

Let the amount x be lent at r1% and remaining (P - x) at r2%, and let the sum of interests be I. Then, I = ${x × r_1 × 5}/100$ + ${(P - x) × r_2 × 5}/100$, which simplifies to 100I = 5 × ($x × (r_1 - r_2) + P × r_2$). Putting r_{1} = 13, r_{2} = 6, P = 1100, I = 715, we get x = Rs. 1100.