Question

Anuj, Bheem and Charles invest in the ratio \(2:4:5\). After 6 months Anuj withdrew \(\frac{1}{4}\) of his capital. Bheem withdrew \(\frac{1}{4}\) of his initial capital at the end of every quarter, while Charles added \(\frac{2}{5}\) of his initial capital at the end of every quarter. If the annual profit is Rs. 98000, what is Bheem's share?

• A. Rs. 14000
• B. Rs. 18000
• C. Rs. 20000
• D. Rs. 21000

Hint:

Instead of summing capital-months quarter by quarter, try computing each partner's average capital over the year and multiplying by 12.

Answer 1

The Correct Option is C

Take initial capitals \(2k, 4k, 5k\). Using quarter units (each 3 months): Anuj = \(2k,2k,1.5k,1.5k\Rightarrow\) capital-months \(3(2+2+1.5+1.5)k=21k\). Bheem loses \(1k\) per quarter: \(4k,3k,2k,1k\Rightarrow 3(10k)=30k\). Charles gains \(2k\) per quarter: \(5k,7k,9k,11k\Rightarrow 3(32k)=96k\). Total \(=21k+30k+96k=147k\). Bheem's share \(=\frac{30}{147}\times 98000=20000\). Correct option: Rs. 20000.