The simple interest on a certain sum is $$11\frac{1}{9}$$ % of the sum and the number of years is equal to the rate percent per annum. What will be the simple interest on a sum of ₹ 12600 at the same rate for $$2\frac{4}{5}$$ years?

Let rate of interest = time period = $$r$$

Let sum = Rs. $$9x$$, => Simple interest = Rs. $$\frac{1}{9}\times9x=x$$

Simple interest = $$\frac{P\times r\times t}{100}$$

=> $$\frac{9x\times r\times r}{100}=x$$

=> $$r^2=\frac{100}{9}$$

=> $$r=\sqrt{\frac{100}{9}}=\frac{10}{3}\%$$

$$\therefore$$ Simple interest on a sum of ₹ 12600 at the same rate for $$2\frac{4}{5}$$ years

= $$\frac{12600}{100}\times\frac{10}{3}\times\frac{14}{5}$$

= $$42\times28=Rs.$$ $$1176$$

=> Ans - (C)