Question:hard

M and N start a business with respective capitals of Rs. 35,000 and Rs. 22,000. M withdrew an amount of Rs. 1,000 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 N?

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Add up each partner's capital for all 13 months (an arithmetic progression, since Rs. 1,000 changes hands every month) to get the profit-sharing ratio, then split Rs. 85,500 in that ratio.
Updated On: Jul 20, 2026
  • Rs. 22,500
  • Rs. 33,000
  • Rs. 43,500
  • Rs. 46,000
  • Rs. 48,500
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The Correct Option is C

Solution and Explanation

Instead of listing all 13 months, use the average capital method.
M's capital forms an AP from 34000 down to 22000, so his average capital over the 13 months is simply the average of the first and last terms:
$$\bar{M}=\frac{34000+22000}{2}=28000$$
N's capital forms an AP from 23000 up to 35000, so his average capital is:
$$\bar{N}=\frac{23000+35000}{2}=29000$$
Since both partners stayed invested for the same 13 months, the profit-sharing ratio is just the ratio of these average capitals:
$$M:N=28000:29000=28:29$$
N's share of the total profit is then:
$$N=85500\times\frac{29}{28+29}=85500\times\frac{29}{57}=1500\times29=43500$$\[\boxed{Rs.\ 43{,}500}\]
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