Akshay has ₹1218 with him. He divided it amongst his sons Arjun and Kartik and asked them to invest it at 10% rate of interest compounded annually. It was seen that Arjun and Kartik got same amount after 12 and 13 years respectively. How much (in ₹) did Akshay give to Kartik?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 580.
Let Arjun’s principal = P
Kartik’s principal = 1218 – P
Given: Amount after 12 years for Arjun = Amount after 13 years for Kartik
Rate = 10%
A = P × (1 + r)t
So, P × (1.1)12 = (1218 – P) × (1.1)13
Divide both sides by (1.1)12:
P = (1218 – P) × 1.1
P = 1218 × 1.1 – P × 1.1
P + 1.1P = 1218 × 1.1
2.1P = 1339.8
P = 1339.8 / 2.1 = 638
Kartik’s share = 1218 – 638 = ₹580