Question

P,Q,R are partner. Q retired. Calculate the gain ratio if Old ratio was 2:2:1 and New Ratio is 2:1.​

Answer 1

ANSWER :

• ❖ If P,Q and R are partner and Q retired; the gain ratio between P and R is 2 : 1 if Old ratio was 2 : 2 : 1 and New Ratio is 2 : 1.

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SOLUTION :

❒ Given :-

• Old ratio of P, Q and R = 2 : 2 : 1

• New ratio of P and R = 2 : 1

❒ To Calculate :-

• Gaining Ratio between P and R = ?

❒ Calculation :-

• Old ratio of P, Q and R = 2 : 2 : 1

➝ P's share of Profit = $\sf{\dfrac{2}{5}}$

➝ R's share of Profit = $\sf{\dfrac{1}{5}}$

• New ratio of P and R = 2 : 1

➝ P's share of Profit = $\sf{\dfrac{2}{3}}$

➝ R's share of Profit = $\sf{\dfrac{1}{3}}$

Thus,

❍ P's gain = $\sf{\dfrac{2}{3}}$ - $\sf{\dfrac{2}{5}}$

➙ P's gain = $\sf{\dfrac{10 - 6}{15}}$

➙ P's gain = $\sf{\dfrac{4}{15}}$

And,

❍ R's gain = $\sf{\dfrac{1}{3}}$ - $\sf{\dfrac{1}{5}}$

➙ R's gain = $\sf{\dfrac{5 - 3}{15}}$

➙ R's gain = $\sf{\dfrac{2}{15}}$

∴ The gaining ratio bwtween P and R = $\sf{\dfrac{4}{15}}$ : $\sf{\dfrac{2}{15}}$

➜ Gaining Ratio = 4 : 2

➜ Gaining Ratio = 2 : 1 ★

• Hence, the gain ratio between P and R is 2 : 1.