A sum of money is accumulating at compound interest at a certain rate of interest. If simple interest instead of compound were reckoned, the interest for the first two years would be diminished by ₹20 and that for the first three years by ₹61. What is the sum?

Difference between S.I. and C.I. for two years = $$\frac{Pr^2}{100^2}=20$$ ------------(i)

Difference for three years = $$\frac{Pr^2}{100^2}(3+\frac{r}{100})=61$$ -----------(ii)

Substituting value from equation (i) in equation (ii), => $$20\times(3+\frac{r}{100})=61$$

=> $$3+\frac{r}{100}=\frac{61}{20}=3.05$$

=> $$\frac{r}{100}=3.05-3=0.05$$

=> $$r=5\%$$

Substituting back in equation (i), => $$P\times\frac{25}{100\times100}=20$$

=> $$P=20\times400=Rs.$$ $$8,000$$

=> Ans - (C)