X and Y sharing profits in the ratio of 7 : 3, admit Z for 3/7 share in the…

2025

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:

  1. A.

    7 : 3 : 3

  2. B.

    4 : 2 : 3

  3. C.

    14 : 6 : 15

  4. D.

    29 : 11 : 30

Attempted by 4 students.

Show answer & explanation

Correct answer: D

Concept: When a new partner is admitted, the new partner's share is carved out of the older partners' shares — the portion each gives up is called their sacrifice. Each old partner's new share = original share − sacrifice, and the new partner's share = the sum of the sacrifices made in their favour. All shares must first be expressed as fractions of the same whole (the entire firm) before they can be subtracted or compared.

  1. Convert the old ratio X : Y = 7 : 3 into shares of the whole firm: X = 7/10, Y = 3/10.

  2. X sacrifices 2/7 of the firm and Y sacrifices 1/7 of the firm, both in favour of Z.

  3. X's new share = old share − sacrifice = 7/10 − 2/7. Using LCM(10, 7) = 70: 49/70 − 20/70 = 29/70.

  4. Y's new share = 3/10 − 1/7 = 21/70 − 10/70 = 11/70.

  5. Z's share = 2/7 + 1/7 = 3/7, which equals 30/70 — matching the 3/7 share stated for Z in the question.

  6. New ratio X : Y : Z = 29/70 : 11/70 : 30/70 = 29 : 11 : 30.

Cross-check: 29 + 11 + 30 = 70 = 70/70, so the three shares exactly account for the whole firm, and Z's derived share (30/70 = 3/7) matches the 3/7 admitted share given in the question — confirming that the new ratio of X, Y and Z is 29 : 11 : 30.

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