Question

D, E and F were partners in a firm sharing profits and losses in the ratio of 2 : 3 : 5. G was admitted as a new partner for \(\frac{1}{5}\)th share in the profits of the firm. G acquired his share entirely from F. The new profit sharing ratio among D, E, F and G will be:

• A. 5 : 2 : 2 : 1
• B. 2 : 3 : 3 : 2
• C. 3 : 3 : 2 : 2
• D. 4 : 3 : 2 : 1

Hint:

When a new partner gets his share entirely from an existing partner, deduct that share only from that partner's portion, keeping others' shares unchanged.

Answer 1

The Correct Option is A

Old ratio of D : E : F = 2 : 3 : 5
Total parts = \(2 + 3 + 5 = 10\)
So, D = \(\frac{2}{10}\), E = \(\frac{3}{10}\), F = \(\frac{5}{10}\)
G is admitted for \(\frac{1}{5} = \frac{2}{10}\) share, which is completely given by F.
New share of G = \(\frac{2}{10}\) (from F)
New share of F = \( \frac{5}{10} - \frac{2}{10} = \frac{3}{10} \)
D and E's shares remain unchanged.
So, New Ratio:
D = \(\frac{2}{10}\), E = \(\frac{3}{10}\), F = \(\frac{3}{10}\), G = \(\frac{2}{10}\)
Now express in whole numbers:
L.C.M. of denominators = 10
So ratio becomes: \(2 : 3 : 3 : 2\)
But this doesn’t match any given option. Let's double-check the share from F to G.
F originally had \(\frac{5}{10}\), gave away \(\frac{2}{10}\), so remains with \(\frac{3}{10}\).
New ratio: D = \(\frac{2}{10}\), E = \(\frac{3}{10}\), F = \(\frac{3}{10}\), G = \(\frac{2}{10}\)
Wait — there’s a miscalculation. Let’s recalculate properly with clear steps.
Let total profit = 1.
G gets \(\frac{1}{5} = 0.2\), and he gets this from F.
F’s new share = \( \frac{5}{10} - 0.2 = 0.5 - 0.2 = 0.3 \)
D’s share = \(\frac{2}{10} = 0.2\), E’s share = \(\frac{3}{10} = 0.3\), G’s = 0.2
Now the new shares: D = 0.2, E = 0.3, F = 0.3, G = 0.2
Convert to ratio form by multiplying all by 10:
D : E : F : G = 2 : 3 : 3 : 2
This matches option (B) not (A). Hence, the correct answer is:
% Corrected Answer Correct Answer: (B) 2 : 3 : 3 : 2