Some part of Rs.9500 was lent at the rate of 15% per annum simple interest and the remaining part at the rate of 20% per annum simple interest. The total interest received after $$\frac{3}{2}$$ years is Rs.2565. What is the ratio of money lent at the rate of 15% and 20%?

Let sum lent for 15% = Rs. $$100x$$ and sum lent for 20% = Rs. $$(9500-100x)$$

Time period = $$\frac{3}{2}=1.5$$ years

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

According to ques,

=> $$\frac{100x\times15\times1.5}{100}+\frac{(9500-100x)\times20\times1.5}{100}=2565$$

=> $$22.5x+(95-x)\times30=2565$$

=> $$22.5x+(95\times30)-30x=(95\times27)$$

=> $$-7.5x=95(27-30)$$

=> $$x=\frac{95\times3}{7.5}=38$$

$$\therefore$$ Required ratio = $$\frac{100\times38}{9500-(100\times38)}$$

= $$\frac{3800}{5700}=2:3$$

=> Ans - (C)