Question

P & Q are partners sharing profits and losses in the ratio of 4:3. They decided to admit R for one-sixth share in profit. Calculate their new PSR. Also calculate Sacrifice Ratio

Answer 1

Explanation:

let the total work be 1

r admit for 1/6 share

remaing 1-1/6=5/6

p new ratio will 5/6*4/7=20/42

q new ratio will 5/6*3/7=15/42

r new share will 1/6 multiply by 7 numerator and deminometer =7/42

p:q:r =20:15:7

sr ratio old-new

p 4/7-20/42 =4/42

q 3/7-15/42 = 3/42

4:3 is sacrifice ratio

Answer 2

Answer:

• New Profit Sharing Ratio =
• P : Q : R = 20 : 15 : 7

• Sacrifice Ratio =
• P : Q = 4 : 3

Explanation:

Old Ratio =

P : Q = 4 : 3

• P's share = $\dfrac{4}{7}$

• Q's share = $\dfrac{3}{7}$

They decided to admit R for one-sixth share in profit :

Let,

Total Share of Profit = 1

• R's share = $\dfrac{1}{6}$

Remaining share =

$\longrightarrow$$1 \: - \: \dfrac{1}{6} = \dfrac{5}{6}$

• P's new share =

$\longrightarrow$ $\dfrac{5}{6} \: \times \: \dfrac{4}{7}$

$\longrightarrow$$\dfrac{20}{42}$

• P's new share = $\dfrac{20}{42}$

• Q's new share =

$\longrightarrow$$\dfrac{5}{6} \: \times \: \dfrac{3}{7}$

$\longrightarrow$ $\dfrac{15}{42}$

• Q's new share = $\dfrac{15}{42}$

• R's Share =

$\longrightarrow$$\dfrac{1}{6} = \dfrac{7}{42}$

• R's Share = $\dfrac{7}{42}$

New Profit Sharing Ratio =

P : Q : R = 20 : 15 : 7

★ Sacrifice Ratio :

Sacrifice Ratio = Old Ratio - New Ratio

P's Sacrifice =

$\longrightarrow$ $\dfrac{4}{7} - \dfrac{20}{42}$

$\longrightarrow$ $\dfrac{24 \: - \: 20}{42} \: = \: \dfrac{4}{42}$

Q's Sacrifice =

$\longrightarrow$ $\dfrac{3}{7} - \dfrac{15}{42}$

$\longrightarrow$ $\dfrac{18 \: - \: 15}{42} = \dfrac{3}{42}$

Sacrifice Ratio =

P : Q = 4 : 3

∴

• New Profit Sharing Ratio =
• P : Q : R = 20 : 15 : 7

• Sacrifice Ratio =
• P : Q = 4 : 3