Question

Calculate the New Ratio.

Crow and Swan are partners sharing profits in the ratio of 5:3. Peacock joins the firm as a new partner, Crow gives 1/4th of his share and Swan gives 2/5th of his share to the new partner.

Answer 1

Question:

• Calculate the New Ratio. Crow and Swan are partners sharing profits in the ratio of 5:3. Peacock joins the firm as a new partner, Crow gives 1/4th of his share and Swan gives 2/5th of his share to the new partner.

Required Solution:

• Old ratio of crow = 5/8
• Old ratio of swan = 3/8

We know that,

✪ Sacrificing ratio = Old ratio - Surrender ratio ✪

So,

➻ Crow's sacrifice = 5/8 × 1/4

➻ Crow's sacrifice = (5 × 1)/(8 × 4)

➻ Crow's sacrifice = 5/32

Also,

➻ Swan's sacrifice = 3/8 × 2/5

➻ Swan's sacrifice = (3 × 2)/(8 × 5)

➻ Swan's sacrifice = 6/40

We know that,

✪ New ratio = Old ratio - Sacrificing ratio ✪

So,

➻ Crow's new ratio = 5/8 - 5/32

➻ Crow's new ratio = (5 × 4)/(8 × 4) - 5/32

➻ Crow's new ratio = 20/32 - 5/32

➻ Crow's new ratio = (20 - 5)/32

➻ Crow's new ratio = 15/32

Also,

➻ Swan's new ratio = 3/8 - 6/40

➻ Swan's new ratio = (3 × 5)/(8 × 5) - 6/40

➻ Swan's new ratio = 15/40 - 6/40

➻ Swan's new ratio = (15 - 6)/40

➻ Swan's new ratio = 9/40

Now,

➻ Peacock's new ratio = Crow's sacrifice + Swan's sacrifice

➻ Peacock's new ratio = 5/32 + 6/40

➻ Peacock's new ratio = (5 × 5)/(32 × 5) + (6 × 4)/(40 × 4)

➻ Peacock's new ratio = 25/160 + 24/160

➻ Peacock's new ratio = (25 -)+ 24)/160

➻ Peacock's new ratio = 49/160

New profit sharing ratio b/w crow, swan and peacock,

➻ 15/32:9/40:49/160

➻ (15 × 5)/(32 × 5):(9 × 4)/(40 × 4):49/160

➻ 75/160:36/160:49/160

➻ 75:36:49

• Henceforth, new profit sharing ratio b/w crow, swan and peacock is 75:36:49.

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Answer 2

➩Given:-

• Crow and Swan are partners in a firm, sharing profits and losses in the ratio 5:3
• Peacock joins the firm
• Crows given 1/4th of his share to peacock and Swan gives 2/5th of his share to peacock

➩To Find:-

• The New profit sharing ratio = ?

➩Solution:-

• Crows old share = 5/8
• Swans old share = 3/8
• Peacock share = Sacrifice from Crow + Sacrifice from Swan

➞ From Crow peacock gets :

• 5/8 × 1/4 = 5/32

➞ From Swan peacock gets :

• 3/8 × 2/5 = 6/40

✧ Calculation of the new profit sharing ratio

• New Ratio = Old Ratio - Ratio Surrendered

➞ For Crow :

• New Ratio = 5/8 - 5/32 = (20-5)/32 = 15/32, or 600/1280

➞ For Swan :-

• New Ratio = 3/8 - 6/40 = (15-36)/40 = 9/40 or, 288/1280

➞ For Peacock :-

• New Ratio = 5/32 + 6/40 = (200+192)/1280 = 392/1280

Therefore the New Profit-Sharing Ratio is 600:288:392 or 75:36:49 !

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