A sum of Rs. 2800 is divided into two parts in such a way that the interest on both the parts is equal. If the first part is lent at 9% p.a for 5 years and second part is for 6 years at 10% p.a., find the two sums.

Let the principal sum for first part = Rs. $$x$$ and for second part = Rs. $$(2800-x)$$

Simple interest = $$\frac{P\times R\times T}{100}$$

First part is lent at 9% for 5 years and second part at 10% for 6 years

According to ques,

=> $$\frac{x\times9\times5}{100}=\frac{(2800-x)\times10\times6}{100}$$

=> $$45x=(2800-x)\times60$$

=> $$3x=(2800-x)\times4$$

=> $$3x=11200-4x$$

=> $$3x+4x=7x=11200$$

=> $$x=\frac{11200}{7}=1600$$

Other sum = $$2800-1600=1200$$

$$\therefore$$ The two sums are = Rs. 1600 and Rs. 1200

=> Ans - (B)