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Numerical Questions · Q3

Q.X and Y are partners sharing profits in 5:3 ratio admitted Z for 1/10 share which he acquired equally from X and Y. Calculate new profit sharing ratio?

Chhattisgarh CgbseTextbookSubjective· 3mImportance★★★★★
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✓ Free question

The new profit-sharing ratio among X, Y, and Z is 23:13:4, calculated by Z acquiring 1/20 from each of X and Y.

When a new partner is admitted, the old partners sacrifice a portion of their share. The key is to determine exactly how much each old partner gives up. Here, Z gets 1/10 of the total profit, and he acquires this equally from X and Y. That means Z takes half of his share from X and half from Y.

So, Z's share = 1/10. He takes 1/20 from X and 1/20 from Y.

Now, the old ratio of X and Y is 5:3. Their original shares were:

  • X's old share = 5/8
  • Y's old share = 3/8

After sacrificing:

  • X's new share = 5/8 - 1/20
  • Y's new share = 3/8 - 1/20
  • Z's new share = 1/10

Let's compute these fractions with a common denominator. The LCM of 8, 20, and 10 is 40.

X's new share = (5/8) - (1/20) = (25/40) - (2/40) = 23/40

Y's new share = (3/8) - (1/20) = (15/40) - (2/40) = 13/40

Z's new share = 1/10 = 4/40

So the new ratio is 23:13:4.

Watch out

A common mistake is to think Z takes 1/10 from X and 1/10 from Y, which would total 2/10. The phrase "acquired equally from X and Y" means Z's total share of 1/10 is split equally between the two sacrifices, not that each gives 1/10.

Tip

When a new partner acquires his share from old partners in a given proportion, always first find the individual sacrifice amounts. Then subtract each from the old partner's original share.

✓Final answer

The new profit-sharing ratio is X : Y : Z = 23 : 13 : 4.

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