Mahesh has Rs. 1617 with him. He divided it amongst his sons Vijay and Ajay and asked them to invest it at 10% rate of interest compounded annually. It was seen that Vijay and Ajay got same amount after 19 and 20 years respectively. How much (in Rs. ) did Mahesh give to Vijay?

Correct option is C

Given:
Total money Mahesh has = Rs. 1617
Rate of interest = 10% per annum (compounded annually)
Vijay invested for 19 years
Ajay invested for 20 years
Final amounts after respective years are the same
Formula Used:
Compound Interest (annual compounding):
​$$\text{Amount} = P\left(1 + \frac{R}{100}\right)^n$$​​
Solution:
Let Money given to Vijay = V and Money given to Ajay = A
Condition of equal amounts:
​$$V(1.1)^{19} = A(1.1)^{20}$$​​
Dividing both sides by $$(1.1)^{19}$$​:
V = A × 1.1
Also, V + A = 1617
Substitute V = 1.1A:
1.1A + A = 1617
2.1A = 1617
A = 1617 / 2.1 = 770
Now, V = 1.1 × 770 = 847
Mahesh gave Rs. 847 to Vijay.