Question

Divide Rs. 3903 between Amar and Akbar such that Amar’s share at the end of 7 years is equal to Akbar’s share at the end of 9 years at 4% p.a. rate of compound interest.
Options

Amar = Rs. 2028, Akbar = Rs. 1875

Amar = Rs. 2008, Akbar = Rs.1000

Amar = Rs. 2902, Akbar = Rs. 1001

Amar = Rs. 2600, Akbar = Rs. 1303

Answer 1

Amar = Rs. 2028, Akbar = Rs. 1875

Step-by-step explanation:

Let say Amar Share  = P  Rs

then Akbar Share = 3903 - P

using A = P(1 + R/100)ⁿ

for Amar   P = P

R = 4 %

n = 7

Amar Amount after 7 Years  = P(1 + 4/100)⁷

for Akbar

P = 3903 - P

R = 4 %

n = 9

Akbar Amount after 9 Years  = (3903-P)(1 + 4/100)⁹

P(1 + 4/100)⁷ = (3903-P)(1 + 4/100)⁹

=> P = (3903 - P)(1.04)²

=> P = 3903 * 1.04²  - 1.04²P

=>  P = 3903 * 1.0816‬  - 1.0816‬P

=> 2.0816‬P = 3903 * 1.0816‬

=> P = 2028

Amar Share = 2028 Rs

Akbar Share = 3903 - 2028  = 1875  Rs

Amar = Rs. 2028, Akbar = Rs. 1875

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