Ashok has ₹1612 with him. He divided it amongst his sons Raj and Varun and asked them to invest it at 8% rate of interest compounded annually. It was seen that Raj and Varun got same amount after 16 and 17 years respectively. How much (in ₹) did Ashok give to Raj?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 837.
Let Raj’s share = R
Varun’s share = 1612 − R
Raj’s amount after 16 years = R × (1 + 8/100)16
Varun’s amount after 17 years = (1612 − R) × (1.08)17
Given both amounts equal:
R × (1 + 8/100)16 = (1612 − R) × (1.08)17
⇒ R = (1612 − R) × 1.08
⇒ R = 1612 × 1.08 − 1.08R
⇒ R + 1.08R = 1612 × 1.08
⇒ 2.08R = 1740.96
⇒ R = 1740.96 / 2.08 = 837