A man borrows some money at 3% simple interest per annum and lends it to somebody at 5% interest to be compounded annually. By this he makes a profit of Rs. 541 at the end of 3 years. The money he borrowed was

Let amount that the man borrowed = Rs. $$100x$$

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

Interest the man need to return to the source at 3% in 3 years

= $$A=\frac{100x\times3\times3}{100}=Rs.$$ $$9x$$

Compound interest at 5% = $$P[(1+\frac{R}{100})^T-1]$$

Similarly, interest the man get from other person = $$A'=100x[(1+\frac{5}{100})^3-1]$$

= $$100x[(\frac{21}{20})^3-1]$$

= $$100x(\frac{9261-8000}{8000})$$

= $$100x\times\frac{1261}{8000}=Rs.$$ $$15.7625x$$

According to ques,

=> $$A'-A=541$$

=> $$15.7625x-9x=6.7625x=541$$

=> $$x=\frac{541}{6.7625}=80$$

$$\therefore$$ Amount the man borrowed = $$100\times80=Rs.$$ $$8,000$$

=> Ans - (A)