₹ 13,540 is to be divided between Kamal and Sunita such that Kamal's share at the end of 5 years may be equal to Sunita's share at the end of 7 years. If the rate of interest is 8% per annum compounded annually, then Kamal's share is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. ₹ 7,290.
Given:
₹ 13,540 is to be divided between Kamal and Sunita
Kamal's share at the end of 5 years may be equal to Sunita's share at the end of 7 years.
The rate of interest is 8% per annum
Formula used:
Amount = P(1 + R/100)T ---- (1)
Compound interest = Amount - Principle
Where P = principle, R = rate and T = time
Calculations:
Let the amount with kamal be x
Amount with sunita = (13540 - x)
Using equation (1), we get
Amount of kamal at the end of 5 years = Amount of sunita at the end of 7 years
⇒ x(1 + 8/100)5 = (13540 - x)(1 + 8/100)7
⇒ x/(13540 - x) = (1 + 8/100)2
⇒ x/(13540 - x) = (27/25)2
⇒ x/(13540 - x) = 729/625
⇒ 625x = 9870660 - 729x
⇒ 1354x = 9870660
⇒ x = 7290