Question

Krishna, Raja and Sony share profits as 1/2 to Krishna, 1/3 to Raja and 1/6 to

Sony. Sony retires. Calculate the gaining ratio of Krishna and Raja.​

Answer 1

Explanation:

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Answer 2

Given :

Proportion in Sharing Profits among partners = $\sf \: \frac{1}{2}: \frac{1}{3} : \frac{1}{6}$

Sony retires.

To Find :

Gaining Ratio Of Krishna and Raja

Formula To Find :

${\underline{\boxed{\bf{Gaining \:ratio \: = New \: share \: - Old \: share}}}}$

Solution :

Old Ratio Of Partners :

$\sf \to \: In \: Proportion \: = \frac{1}{2}: \frac{1}{3} : \frac{1}{6}$

To find old Ratio , we have to make all the denominators same to 6.

$\sf \to \: \frac{1 \times 3}{2 \times 3} : \frac{1 \times 2}{3 \times 2} : \frac{1 \times 1}{6 \times 1}$

$\sf \to \: \frac{3}{6} : \frac{2}{6} : \frac{1}{6}$

$\sf \to \: 3: 2 : 1$

Old ratio Of Krishna , Raja , and Sony : 3:2:1

Sony Retires,

New Ratio Of continuing Partners :

$\sf \to \: old \: ratio \: = 3 : 2 : 1$

$\sf \to \: new \:ratio \: of \: partners \: = 3: 2$

Gaining Ratio :

• New Ratio - Old ratio

Gaining ratio of Krishna :

$\sf \to \: \frac{3}{5} - \frac{3}{6}$

$\to \sf \: \frac{3 \times 6 - 3 \times 5}{5 \times 6}$

$\sf \to \: \frac{18 - 15}{30}$

$\bf \to \: \frac{3}{20}$

Gaining Ratio Of Raja :

$\sf \to \: \frac{2}{5} - \frac{2}{6}$

$\sf \to \: \frac{2 \times 6 - 2 \times 5}{6 \times 5}$

$\sf \to \: \frac{12 - 10}{5}$

$\bf \to \: \frac{2}{30}$

$\bullet \: \sf \frac{3}{30} : \frac{2}{30} = \: 3:2$

$\therefore \sf \: gaining \: ratio \: of \: continuing \: partners = 3 : 2$