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X and Y sharing profits in the ratio of 7 : 3, admit Z for 3/7 share in the new firm in which he takes 2/7 from X and 1/7 from Y. The new ratio of X, Y and Z will be :

This question was previously asked in
UGC Paper 2: Commerce July 2018
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  1. 7 : 3 : 3
  2. 4 : 2 : 3
  3. 14 : 6 : 15
  4. 29 : 11 : 30

Answer (Detailed Solution Below)

Option 4 : 29 : 11 : 30
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Detailed Solution

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Explanation:

Old Ratio = 7:3

Z's Share = 3/7

X's Sacrifice In Favor Of Z = 2/7

X's Sacrifice Ratio = Old Ratio - New Ratio

2/7 = 7/10 - New Ratio

New Ratio = 7/10 - 2/7

X's New Ratio = 29/70

Y's Sacrifice In Favor Of Z = 1/7

Y's Sacrifice Ratio = Old Ratio - New Ratio

1/7 = 3/10 - New Ratio

New Ratio = 3/10 - 1/7

Y's New Ratio = 11/70

New Ratio = X : Y : Z

New Ratio = 29/70 : 11/70 : 3/7

New Ratio = 29 : 11 : 30

Therefore, if X and Y sharing profits in the ratio of 7 : 3, admit Z for 3/7 share in the new firm in which he takes 2/7 from X and 1/7 from Y. The new ratio of X, Y, and Z will be 29: 11: 30.

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