Profit Sharing Problems - Ratios and Calculations

Profit Sharing Problem (a)

• Lucy and Zeny initially share profits in a 4:3 ratio
• Allen acquires a 20% share of the profits
• Allen acquires this share from Lucy and Zeny in a 1:2 ratio
• This means Lucy sacrifices 1/3 of her initial share, and Zeny sacrifices 2/3 of her initial share
• Calculate the new shares:
  • Lucy: (4/7) * (2/3) = 8/21
  • Zeny: (3/7) * (1/3) = 1/7
  • Allen: 20/100 = 1/5
• The new profit-sharing ratio is 8:3:7

Profit Sharing Problem (b)

• Partners A, B, and C share profits in a 3:2:2 ratio
• New partner D acquires a 1/5 share of the profits
• D acquires this share from A, B, and C in a 2:2:1 ratio
• This means A sacrifices 2/5 of his initial share, B sacrifices 2/5 of his initial share, and C sacrifices 1/5 of his initial share.
• Calculate the new shares:
  • A: (3/7) * (3/5) = 9/35
  • B: (2/7) * (3/5) = 6/35
  • C: (2/7) * (4/5) = 8/35
  • D: 1/5
• The new profit-sharing ratio is 9:6:8:7