An amount was lent for one year at the rate of 10% per annum compounding annually had the compounding been done half yearly, the interest would have increased by 80. What was the amount (in Rs) lent?

Let the amount rent = Rs. $$100x$$

Rate of interest = 10% and time period = 1 year

Amount if compounded annually = $$P(1+\frac{r}{100})^T$$

and if compounded half yearly = $$P(1+\frac{r}{200})^{2T}$$

According to ques, required difference :

=> $$[100x(1+\frac{10}{200})^2]-[100x(1+\frac{10}{100})^1]=80$$

=> $$[100x\times(\frac{21}{20})^2]-[100x\times(\frac{11}{10})]=80$$

=> $$\frac{441x}{4}-110x=80$$

=> $$\frac{441x-440x}{4}=80$$

=> $$x=80\times4=320$$

$$\therefore$$ Sum lent = $$100\times320=Rs.$$ $$32,000$$

=> Ans - (B)