Question

A and B are partners in the ratio of 5 :4 . they admit C for 1/10th shares, which the acquires in equal proportion from both. Find the new profit sharing ratio

Answer 1

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Answer 2

Answer:

Given :

• Old Ratio Of Partners = 5 : 4

• Admit C for ⅒ th Share.

• Acquires equal proportion from both

To Find :

• New Profit Sharing Ratio - ?

Solution :

Here, the question clearly says in relative proportion that, C is admitted for ⅒ th share. Already the parthers sharing profits in 5:4 ( 5 + 4 = 9 ) So, C has 1 share. 5 : 4 : 1 = New Profit Sharing Ratio.

OR Finding by acquiring Equal proportion from both ;

Acquires ⅒ from both means ⅕ from A and B :

New Share Of A :

Old Ratio = 5 ( 5/9 )

$\sf \to \: \frac{5}{9} - \frac{1}{5}$

$\to\sf \: \frac{5 \times 5 - 9 \times 1}{9\times5}$

$\sf \to \: \frac{25 - 9}{45}$

$\bf \to \: \frac{16}{45}$

New Share Of B :

Old ratio = 4 ( 4 / 9 )

$\sf \to \: \frac{4}{9} - \frac{1}{5}$

$\sf \to \: \frac{4 \times 5 - 9 \times 1}{9 \times 5}$

$\sf \to \: \frac{20 - 9}{45}$

$\bf \to \: \frac{11}{45}$

Share Of C :

$\sf \to \: \frac{1}{10}$

$\sf \to \: \frac{16 + 11}{45}$

$\sf \to \: \frac{27}{45} = 45 - 27$

$\bf \to \: 18 \: = \frac{18}{45}$

$\bullet \sf \: \: \frac{16}{45} : \frac{11}{45} : \frac{18}{45}$

= 16 : 11 : 18

$\therefore \sf New \: Ratio \: of \:Partners \: = 16: 11: 18$