Question

P and Q are partners sharing profits and losses in the ratio of 2:1. They admit R for 1/6 share in future profits . Calculate the new ratio.
a)1:1
b)4:2
c)10:5:3
d)None of these​

Answer 1

Answer:

Option (c) 10 : 5 : 3

Explanation:

★ Old Ratio :

P : Q = 2 : 1

• P's Share = 2/3
• Q's Share = 1/3

They admit R for 1/6 share in future profits

• R's Share = 1/6

To find :

• Calculate the New Ratio.

Solution :

Let,

Total Profit of all Partners = 1

So,

• R's Share = 1/6

★ Remaining Share :

1 - 1/6 = 5/6

★ New Profit Sharing Ratio :

• P's New Share =

⇒ 2/3 × 5/6 = 10/18

• Q's New Share =

⇒ 1/3 × 5/6 = 5/18

• R's Share =

⇒ 1/6 = 3/18

New Profit Sharing Ratio =

• P : Q : R = 10/18 : 5/18 : 3/18
• 10 : 5 : 3

Therefore, Option (c). 10 : 5 : 3

New profit sharing ratio of P, Q and R = 10 : 5 : 3.

Answer 2

Given :-

P and Q are partners sharing profits and losses in the ratio of 2:1. They admit R for 1/6 share in future profits

To Find :-

New Ratio

Solution :-

Total share in old ratio = 2 + 1 = 3

Share of P in old ratio = 2/3

Share of Q in old ratio = 1/3

Now, R is admitted with 1/6 profit

This means, R has been admitted 1/6th of total profit i.e 1

Remaining share for P and Q = 1 - 1/6

Remaining share for P and Q = 6 - 1/6

Remaining share for P and Q = 5/6

Now

Share of P in new ratio = 5/6 × 2/3 = 5 × 2/6 × 3 = 10/18

Share of Q in new ratio = 5/6 × 1/3 = 5 × 1/6 × 3 = 5/18

Share of R in new ratio = 1/6 × 3/3 = 1 × 3/6 × 3 = 3/18

Ratio = 10/18 : 5/18 : 3/18

Ratio = 10 : 5 : 3/18

Ratio = 10 : 5 : 3

Option C is correct