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A, B, and C started a business by investing $3000, $4000, and $5000 respectively. After 6 months, A withdrew $1000, B withdrew $2000, and C withdrew $2500. At the end of the year, the total profit was $7400. Find the share of B in the profit.Options$2400$3600$3200$4000

Question

A, B, and C started a business by investing 3000,3000, 4000, and 5000respectively.After6months,Awithdrew5000 respectively. After 6 months, A withdrew 1000, B withdrew 2000,andCwithdrew2000, and C withdrew 2500. At the end of the year, the total profit was 7400.FindtheshareofBintheprofit.Options7400. Find the share of B in the profit.Options2400360036003200$4000

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Solution

To solve this problem, we need to calculate the capital for each person for the time they invested in the business.

  1. For the first 6 months, A invested 3000,Binvested3000, B invested 4000, and C invested 5000.So,thecapitalsare:A′scapital=5000. So, the capitals are: A's capital = 3000 * 6 = 18000B′scapital=18000 B's capital = 4000 * 6 = 24000C′scapital=24000 C's capital = 5000 * 6 = $30000

  2. After 6 months, A withdrew 1000,Bwithdrew1000, B withdrew 2000, and C withdrew 2500.So,forthenext6months,thecapitalsare:A′scapital=(2500. So, for the next 6 months, the capitals are: A's capital = (3000 - 1000)∗6=1000) * 6 = 12000 B's capital = (4000−4000 - 2000) * 6 = 12000C′scapital=(12000 C's capital = (5000 - 2500)∗6=2500) * 6 = 15000

  3. The total capital for the year for each person is: A's total capital = 18000+18000 + 12000 = 30000B′stotalcapital=30000 B's total capital = 24000 + 12000=12000 = 36000 C's total capital = 30000+30000 + 15000 = $45000

  4. The total capital invested in the business is: Total capital = 30000+30000 + 36000 + 45000=45000 = 111000

  5. The share of each person in the profit is proportional to their total capital. So, B's share in the profit is: B's share = Total profit * (B's total capital / Total capital) = 7400∗(7400 * (36000 / 111000)=111000) = 2400

So, the share of B in the profit is $2400.

This problem has been solved

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