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Ram and Shyam Profit Sharing Partnership

XAT 2012 · Quantitative Ability & Data Interpretation · Hard · Partnership

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Ram and Shyam form a partnership (with Shyam as working partner) and start a business by investing 4000 and 6000 respectively. The conditions of partnership were as follows:

  1. In case of profits till 200,000 per annum, profits would be shared in the ratio of the invested capital.
  2. Profits from 200,001 till 400,000 Shyam would take 20% out of the profit, before the division of remaining profits, which will then be based on ratio of invested capital.
  3. Profits in excess of 400,000, Shyam would take 35% out of the profits beyond 400,000, before the division of remaining profits, which will then be based on ratio of invested capital.

If Shyam's share in a particular year was 367000, which option indicates the total business profit (in rupees) for that year?

  1. A.

    520,000

  2. B.

    530,000

  3. C.

    540,000

  4. D.

    550,000

  5. E.

    None of the above

Answer

D

Explanation

Capital ratio Ram:Shyam = 4000:6000=2:34000:6000 = 2:3. Shyam's share on first 200,000 = 200,000×60%=120,000200,000 \times 60\% = 120,000. On next 200,000 (from 200k to 400k): Shyam gets 20%+80%×60%=20%+48%=68%  ⟹  200,000×68%=136,00020\% + 80\% \times 60\% = 20\% + 48\% = 68\% \implies 200,000 \times 68\% = 136,000. Total Shyam's share from first 400k = 120,000+136,000=256,000120,000 + 136,000 = 256,000. Remaining Shyam's share needed = 367,000−256,000=111,000367,000 - 256,000 = 111,000. On profit above 400,000 (let extra profit be xx): Shyam gets 35%+65%×60%=35%+39%=74%35\% + 65\% \times 60\% = 35\% + 39\% = 74\%. 0.74x=111,000  ⟹  x=150,0000.74 x = 111,000 \implies x = 150,000. Total profit = 400,000+150,000=550,000400,000 + 150,000 = 550,000.

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