Vijay has Rs. 1218 with him. He divided it amongst his sons Ajay and Prakash and asked them to invest it at 10% rate of interest compounded annually. It was seen that Ajay and Prakash got same amount after 14 and 15 years respectively. How much (in Rs. ) did Vijay give to Prakash?

Correct option is B

Given:

Total amount = ₹1218

Ajay's investment time = 14 years

Prakash's investment time = 15 years

Interest rate = 10% p.a. compounded annually

Final amounts received by both = Equal

Formula Used:

Amount on Compound interest = $$P(1 + \frac{r}{100})^t$$​​

where P = principal, r = rate of interest, t = time

Solution:

As we Amount receive is equal,

So,

​$$P_1\left(1+\frac{10}{100}\right)^{14} = P_2\left(1 +\frac{4}{100}\right)^{15}$$​​

​$$P_1(1.1)^{14} = P_2(1.1)^{15}$$​​​​

​$$\implies P_1 : P_2 = 22 : 20$$​​

LetAjay’s share = ₹22x and Prakash's share = ₹20x

22x + 20x = 1218
42x = 1218

x = $$\frac{1218}{42} = 29$$​ 

Prakash's share = ₹29 × 20 = ₹580