Question

Raga and Tala are partners sharing profits and losses in the ratio of 7:3. They

admit Shruti into the partnership. Raga surrenders 1/2nd of his share and Tala 1/4th of her share in favour of Shruti. Calculate new profit sharing ratio of Raga, Tala and Shruti. ​

Answer 1

Explanation:

Solution :

★ Old Ratio :

Raga : Tala = 7 : 3

• Raga's share = 7/10
• Tala's share = 3/10

Raga surrenders share in favour of Shruti =

7/10 × 1/2 = 7/20

Tala surrenders share in favour of Shruti =

3/10 × 1/4 = 3/40

★ New profit sharing ratio :

• Raga's new share =

7/10 - 7/20 = (14 - 7)/20

7/20

• Tala's share =

3/10 - 3/40 = (12 - 3)/40

9/40

• Shruti's share =

7/20 + 3/40 = (14 + 3)/40

17/40

New profit sharing ratio :

• Raga : Tala : Shruti
• 7/20 : 9/40 : 17/40

• 14/40 : 9/40 : 17/40

14 : 9 : 17

Therefore,

New profit sharing ratio of Raga, Tala and Shruti = 14 : 9 : 17.

Answer 2

Information provided with us :

• Raga and Tala are partners sharing profits and losses in the ratio of 7:3
• Shruti is admitted into the partenership
• Raga surrendered 1/2nd of his share
• Whereas Tala surrendered 1/4th of her share in favour of Shruti

What we have to calculate :

• New profit sharing ratio of Raga, Tala and Shruti

Performing Calculations :

• Here in noticing the question we came to knew that the old sharing ratio of profit and loses is of Raga and Tala is 7 : 3

=> Share of Raga = 7 / 7 + 3

=> Share of Raga = 7 / 10

And,

=> Share of Tala = 3 / 3 + 7

=> Share of Tala = 3 / 10

According to the question,

• In the question it is given that Raga surrendered 1/2nd of his share and Tala 1/2nd of his share. So we would be multiplying share of Raga with 1/2 and share of Tala with 1/4

Surrendered share's of Raga and Tala:-

=> Surrendered share of Raga = 7/10 × 1/2

=> Surrendered share of Raga = 7 × 1 / 10 × 2

=> Surrendered share of Raga = 7 / 20

=> Surrendered share of Tala = 3/10 × 1/4

=> Surrendered share of Tala = 3 × 1 / 10 × 4

=> Surrendered share of Tala = 3 / 40

Finding out new profit sharing ratio:-

• Here we would be subtracting surrendered share of Raga and Tala with their shares respectively. i.e., (Old share - Surrendered share)

New share of Raga:-

=> New share of Raga = 7/10 - 7/20

=> New share of Raga = 7 × 2 - 7 / 20

=> New share of Raga = 14 - 7 / 20

=> New share of Raga = 7/20

New share of Tala:-

=> New share of Tala = 3/10 - 3/40

=> New share of Tala = 3 × 4 - 3 / 40

=> New share of Tala = 12 - 3 / 40

=> New share of Tala = 9 / 40

New share of Shruti:-

=> New share of Shruti = 7/20 + 3/40

=> New share of Shruti = 7 × 2 + 3 / 40

=> New share of Shruti = 14 + 3 / 40

=> New share of Shruti = 17/40

New profit sharing ratio of them:

=> Raga : Tala : Shruti

• Keeping their new shares of them here,

=> 7/20 : 9/40 : 17/40

=> 7 × 2 / 20 × 2 : 9/40 : 17/40

=> 14/40 : 9/40 : 17/40

40 would be cancelled off,

=> 14 : 9 : 17

Henceforth, new profit sharing ratio is 14 : 9 : 17