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L, M and N are partners sharing profit and losses in the ratio of 25:15:9 . M retires. It is decided that the profit sharing ratio between remaining partner will be the same as existing between M and N. Calculate Gaining ratio
  • a)
    45:80
  • b)
    45:75
  • c)
    40:75
  • d)
    55:75
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
L, M and N are partners sharing profit and losses in the ratio of 25:1...
Old Share 25 : 15 : 9
L’s share = 25/29
Gain Ratio = 45: 75
Free Test
Community Answer
L, M and N are partners sharing profit and losses in the ratio of 25:1...
Calculation:
The profit sharing ratio between the remaining partners will be the same as the existing ratio between M and N. To calculate the gaining ratio, we need to find the difference between the new profit sharing ratio and the existing profit sharing ratio.

Given:
Existing profit sharing ratio between L, M, and N = 25:15:9

Step 1: Calculate the total of the existing ratio:
Total ratio = 25 + 15 + 9 = 49

Step 2: Calculate the existing share of M and N:
Share of M = (15/49) x Total Profit
Share of N = (9/49) x Total Profit

Step 3: Determine the new profit sharing ratio between L and N:
Since M retires, the new profit sharing ratio will be between L and N. As per the given information, the new ratio will be the same as the existing ratio between M and N, which is 15:9.

Step 4: Calculate the new share of N:
New share of N = (9/24) x Total Profit

Step 5: Calculate the gaining ratio:
Gaining ratio = New share of N - Existing share of N
Gaining ratio = [(9/24) x Total Profit] - [(9/49) x Total Profit]
Gaining ratio = [(441 - 216)/1176] x Total Profit
Gaining ratio = (225/1176) x Total Profit

Now, simplify the gaining ratio:
Gaining ratio = (25/132) x Total Profit

Step 6: Convert the gaining ratio to the required format:
To convert the gaining ratio into the required format, we need to find a common multiple for the numerator and denominator.

Divide both the numerator and denominator by 3:
Gaining ratio = (25/132) x Total Profit = (25/44) x (3/3) x Total Profit
Gaining ratio = (75/132) x Total Profit

Now, the gaining ratio can be expressed as:
Gaining ratio = 75:132

Simplify the ratio by dividing both the numerator and denominator by 3:
Gaining ratio = 25:44

Answer:
Therefore, the gaining ratio between the remaining partners L and N is 25:44, which is equivalent to option 'B' (45:75).
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