Raman invested P for 2 years in scheme A which offered 20% p.a. compound interest (compounded annually). He lent the interest earned from scheme A to Shubh, at the rate of 7.5% p.a. simple interest. If at the end of 2 years, Shubh gave Rs.3,036/- to Raman and thereby repaid the whole amount (actual loan + interest), what is the value of P ?

Let amount invested by Raman $$(P) = Rs.$$ $$100x$$ at 20% interest fro 2 years

Compound interest earned = $$P[(1+\frac{r}{100})^T-1]$$

= $$100x[(1+\frac{20}{100})^2-1]$$

= $$100x[(\frac{6}{5})^2-1]$$

= $$100x\times(\frac{36-25}{25})$$

= $$100x\times\frac{11}{25}=Rs.$$ $$44x$$

Now, Raman lent $$Rs.$$ $$44x$$ to Shubh at 7.5% for 2 years

Total amount under simple interest = $$P+\frac{P\times r\times t}{100}$$

=> $$44x+\frac{44x\times7.5\times2}{100}=3036$$

=> $$44x(1+\frac{15}{100})=3036$$

=> $$44x\times\frac{115}{100}=3036$$

=> $$x=3036\times\frac{100}{115\times44}=60$$

$$\therefore$$ Value of P = $$100\times60=Rs.$$ $$6,000$$

=> Ans - (A)