A sum of Rs. 8400 is divided between A and B such that A's share at the end of 2 years is equal to B's share at the end of 2 years at 15% p.a., interest compounded 8 monthly. What is A's share (in Rs.) in the given sum?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 4400
Given:
A sum of Rs. 8400 is divided between A and B
A's share at the end of 2 years is equal to B's share at the end of 2 years at 15% p.a., interest compounded 8 monthly.
Formula used:
A = P(1 + R/100)T ----- (1)
Where, A = amount, P = principal, R = rate and T = time
Calculations:
Let the amount A receive be x
Amount received by B = 8400 - x
Time when interest compounded 8 monthly (for A) = 3 years
Time when interest compounded 8 monthly (for B) = 4 years
Using equation (1), we get
According to the questions;
⇒ x(1 + 10/100)3 = (8400 - x)(1 + 10/100)4
⇒ x(11/10)3 = (8400 - x)(11/10)4
⇒ 10x = (8400 - x)(11)
⇒ 21x = 8400 × 11
⇒ x = 400 × 11
⇒ x = 4400