Multiple choice

David, Emma, and Frank start a business with initial investments of Rs. 80,000, Rs. 1,20,000, and Rs. 1,60,000, respectively. After 4 months, David invests an additional Rs. 20,000, and Emma withdraws Rs. 40,000. If the profit after one year is Rs. 78,000, what is David's share?

  1. Rs. 17,500

  2. Rs. 19,500

  3. Rs. 21,000

  4. Rs. 21,500

  5. Rs. 23,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

David: 80k*4 + 100k*8 = 320k + 800k = 1120k. Emma: 120k*4 + 80k*8 = 480k + 640k = 1120k. Frank: 160k*12 = 1920k. Ratio = 1120:1120:1920 = 7:7:12. Total parts = 26. David's share = (7/26) * 78000 = 7 * 3000 = 21000.

AI explanation

Using the partnership formula, the profit ratio is determined by the product of investment and time. David's effective capital is (80000 * 4) + (100000 * 8) = 1120000; Emma's is (120000 * 4) + (80000 * 8) = 1120000; and Frank's is 160000 * 12 = 1920000. The ratio of their profit shares is 112 : 112 : 192, which simplifies to 7 : 7 : 12, giving a total of 26 parts. David's share of the Rs. 78,000 profit is (7/26) * 78000, resulting in Rs. 21,000.

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