Question

P and Q are partners. P gets 60% and Q gets 40% of profits R is admitted for 20 paise in a rupee. Find out
new ratio and sacrifice ratio.​

Answer 1

Answer:

Ratio of P and Q

60%:40%

=6:4=3:2

R admitted for 20/100 share means 1/5

Calculation of new ratio

Let total share of profit be 1

R share 1/5

Remaining share 1-1/5=4/5

P new share = 4/5×3/5= 12/25

Q new share = 4/5×2/5= 8/25

P:Q:R

12/25:8/25:1/5

12:8:5

sacrifice ratio = old ratio- new ratio

P= 3/5-12/25= 15-12/25=3/25

Q = 2/5-8/25=10-8/25=2/25

sacrifice ratio = 3/25:2/25=3:2

Answer 2

Answer:

New Profit Sharing ratio =

• P : Q : R
• 12 : 8 : 5

Sacrifice ratio becomes =

• P : Q
• 3 : 2

Explanation:

P get 60 % and Q get 40 %

Profit Sharing Ratio =

P : Q

6 : 4

• P = $\dfrac{6}{10} = \dfrac{3}{5}$
• Q = $\dfrac{4}{10} = \dfrac{2}{5}$

★ According to the Question :

R is admitted for 20 paise in a rupee

So,

R = $\dfrac{20}{100} = \dfrac{1}{5}$

Let,

Total Share of Profit = 1

R's Share = $\dfrac{1}{5}$

Remaining share =

$1 - \dfrac{1}{5} = \dfrac{4}{5}$

P's new Share = $\dfrac{4}{5} \times \dfrac{3}{5} = \dfrac{12}{25}$

⇒ $\dfrac{12}{25}$

Q's new Share =$\dfrac{4}{5} \times \dfrac{2}{5} = \dfrac{8}{25}$

⇒ $\dfrac{8}{25}$

R's Share =$\dfrac{20}{100} = \dfrac{5}{25}$

⇒ $\dfrac{5}{25}$

New Profit Sharing ratio =

• P : Q : R
• 12 : 8 : 5

____________________________

Sacrifice ratio :

Sacrifice ratio = Old ratio - New ratio

P's Sacrifice for R = $\dfrac{3}{5} - \dfrac{12}{25} = \dfrac{3}{25}$

⇒ $\dfrac{3}{25}$

Q's Sacrifice for R = $\dfrac{2}{5} - \dfrac{8}{25} = \dfrac{2}{25}$

⇒ $\dfrac{2}{25}$

Sacrifice ratio becomes =

• P : Q
• 3 : 2

Therefore,

New Profit Sharing ratio =

P : Q : R = 12 : 8 : 5

Sacrifice ratio becomes =

P : Q = 3 : 2