Varun has Rs. 1230 with him. He divided it amongst his sons Ashish and Arun and asked them to invest it at 5% rate of interest compounded annually. It was seen that Ashish and Arun got same amount after 11 and 12 years respectively. How much (in Rs. ) did Varun give to Arun?

Correct option is A

Given:

Total money Varun had = Rs. 1230

Rate of interest (R) = 5% compounded annually

Ashish's investment period  = 11 years

Arun's investment period  = 12 years

Amount received by Ashish = Amount received by Arun

Concept Used:

The compound interest formula:

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

Where:

A is the amount (including interest), P is the principal,

R is the rate of interest, n is the number of years.

Solution:

For Ashish: 

Amount  for Ashish = P(Ashish) × (1.05)¹¹

For Arun:

Amount for Arun = P(Arun) × (1.05)¹²

Since the amounts received by Ashish and Arun were the same:

P(Ashish) × (1.05)¹¹ = P(Arun) × (1.05)¹²

P (Ashish) = P(Arun) × 1.05 

Now, 

We know that; 

P (Ashish) + P(Arun) = 1230

[P(Arun) × 1.05] + P(Arun) = 1230

P(Arun) × [1.05 + 1] = 1230

P(Arun) × 2.05 = 1230

P(Arun) = $$\frac{1230}{2.05}$$​ = 600

Thus, Varun gave Rs. 600 to Arun