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प्रश्न
X and Y are partners sharing profits and losses in the ratio of 3 : 2. They admit Z as a new partner who gets `1/5`th share. Calculate the new profit-sharing ratio in each of the following cases:
- If Z acquires his share from X and Y in their profit-sharing ratio;
- If he acquires `3/20`th from X and `1/20`th from Y;
- If he acquires `1/10`th from X and `1/10`th from Y;
- If he acquires `1/20`th from X and `3/20`th from Y;
- If he acquires his share entirely from X;
- If he acquires his share entirely from Y.
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उत्तर
(i)
Share acquired by Z from X = `3/5 xx 1/5`
= `3/25`
Share acquired by Z from Y = `2/5 xx 1/5`
= `2/25`
X’s new share = `3/5 - 3/25`
= `(3 xx 5)/(5 xx 5) - 3/25`
= `15/25 - 3/25`
= `12/25`
Y’s new share = `2/5 - 2/25`
= `(2 xx 5)/(5 xx 5) - 2/25`
= `10/25 - 2/25`
= `8/25`
Z’s new share = `1/5`
= `(1 xx 5)/(5 xx 5)`
= `5/25`
New Ratios = `12/25 : 8/25 : 5/25` or 12 : 8 : 5
(ii)
X’s new share = `3/5 - 3/20`
= `(3 xx 4)/(5 xx 4)`
= `12/20 - 3/20`
= `9/20`
Y’s new share = `2/5 - 1/20`
= `(2 xx 4)/(5 xx 4) - 1/20`
= `8/20 - 1/20`
= `7/20`
Z’s new share = `1/5`
= `(1 xx 4)/(5 xx 4)`
= `4/20`
New Ratios = `9/20 : 7/20 : 4/20` or 9 : 7 : 4
(iii)
X’s new share = `3/5 - 1/10`
= `(3 xx 2)/(5 xx 2) - 1/10`
= `6/10 - 1/10`
= `5/10`
Y’s new share = `2/5 - 1/10`
= `(2 xx 2)/(5 xx 2) - 1/10`
= `4/10 - 1/10`
= `3/10`
Z’s new share = `1/5`
= `(1 xx 2)/(5 xx 2)`
= `2/10`
New Ratios = `5/10 : 3/10 : 2/10` or 5 : 3 : 2
(iv)
X’s new share = `3/5 - 1/20`
= `(3 xx 4)/(5 xx 4) - 1/20`
= `12/20 - 1/20`
= `11/20`
Y’s new share = `2/5 - 3/20`
= `(2 xx 4)/(5 xx 4) - 3/20`
= `8/20 - 3/20`
= `5/20`
Z’s new share = `1/5`
= `(1 xx 4)/(5 xx 4)`
= `4/20`
New Ratios = `11/20 : 5/20 : 4/20` or 11 : 5 : 4
(v)
If Z acquires his share entirely from X:
X’s new share = `3/5 - 1/5`
= `2/5`
Y’s share = `2/5`
Z’s share = `1/5`
New Ratios = 2 : 2 : 1
(vi)
If Z acquires his share entirely from Y:
X’s new share = `3/5`
Y’s share = `2/5 - 1/5`
= `1/5`
Z’s share = `1/5`
New Ratios = 3 : 1 : 1
