Question

M and N start a business with respective capitals of Rs. 35,000 and Rs. 22,000. M withdrew an amount of Rs. 1000 every month from the business while N put in an additional amount of Rs. 1,000 every month into the business. If they close the business after 13 months after making a profit of Rs. 85,500, then what is the share of M?

• A. Rs. 22,000
• B. Rs. 33,000
• C. Rs. 42,000
• D. Rs. 46,000
• E. Rs. 48,000

Hint:

Work out each partner's total capital-months over the 13 months, then split the profit in that ratio.

Answer 1

The Correct Option is C

M's capital is reduced by Rs. 1,000 every month, and by the \(k\)-th month a total of \(1000k\) has been withdrawn, so his effective capital during month \(k\) is \(35000 - 1000k\), for \(k = 1\) to \(13\).
Sum of M's capital over 13 months = \(13 \times 35000 - 1000(1+2+\cdots+13) = 455000 - 1000 \times 91 = 455000 - 91000 = 364000\).
Similarly, N's capital during month \(k\) is \(22000 + 1000k\), so the sum over 13 months = \(13 \times 22000 + 1000 \times 91 = 286000 + 91000 = 377000\).
Ratio of M's capital to N's capital = \(364000 : 377000 = 28 : 29\) (dividing both by 13000).
Total profit = Rs. 85,500, shared in the ratio 28:29, total parts = 57.
M's share = \(85500 \times \dfrac{28}{57} = 1500 \times 28 = 42000\).
So M's share of the profit is Rs. 42,000.