Anand has ₹1,617 with him. He divided it amongst his sons Anil and Ashok and asked them to invest it at 10% rate of interest per annum, compounded annually. It was seen that Anil and Ashok got same amount after 12 and 13 years, respectively. How much (in ₹) did Anand give to Anil?​

Correct option is A

Given:

Total amount Anand distributed = ₹1617

Rate of interest (compounded annually) = 10% = 0.1

Anil received the money for 12 years, Ashok for 13 years

Final amount received by Anil and Ashok is equal

Formula Used:

Compound interest formula:

A = $$P\left(1 + \frac{R}{100}\right)^n$$​​

If both amounts are equal, we can equate their compound interest expressions to find the principal values.

Solution:

Let $$P_{Anil}$$​ and $$P_{Ashok}$$​ be the principal amounts given to Anil and Ashok respectively.

​$$P_{Anil} + P_{Ashok} = 1617$$​

Now, 

​$$P_{Anil} \cdot (1.1)^{12} = P_{Ashok} \cdot (1.1)^{13}$$​​

​$$P_{Anil} = P_{Ashok} \cdot 1.1$$​​

Substitute $$P_{Anil} = 1.1 \cdot P_{Ashok}$$​ into the total:

​$$1.1 \cdot P_{Ashok} + P_{Ashok} = 1617$$​​

​$$2.1 \cdot P_{Ashok} = 1617$$​​

​$$P_{Ashok} = \frac{1617}{2.1} = \frac{16170}{21} = 770$$​​

​$$P_{Anil} = 1.1 \cdot 770 = 847$$​​

Thus, ₹847 was given to Anil.