The simple interest on a certain sum at 14% per annum for $$3\frac{1}{4}$$ years is ₹3731. What will the amount of the same sum for $$5\frac{1}{2}$$ years at half the earlier rate?

Let the principal sum be Rs. $$P$$

Rate of interest = $$r=14\%$$ and time period = $$t=\frac{13}{4}$$ years

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

=> $$\frac{P\times14\times13}{4\times100}=3731$$

=> $$P=3731\times200\times\frac{1}{91}=Rs.$$ $$8200$$

Now, amount after $$\frac{11}{2}$$ years and at $$7\%$$

= $$8200+(\frac{8200\times7\times11}{2\times100})$$

= $$8200+3157=Rs.$$ $$11357$$

=> Ans - (D)