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16 Nov 2023, 20:53
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A
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A and B started a business with initial investments in the respective ratio of 18:7. After four months from the start of the business, A invested $ 2000 more and B invested $ 7000 more each month. At the end of one year, if the profit was distributed among them in the ratio of 2:1 respectively. What was the total initial investment with which A and B started the business?
A) $ 50,000
B) $ 225,000
C) $1,50,000
D) $ 75,000
A) $ 50,000
B) $ 225,000
C) $1,50,000
D) $ 75,000
17 Jun 2025, 21:52
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Let A's initial investment = 18x and B's initial investment = 7x
For the first 4 months:
A's investment = 18x for 4 months
B's investment = 7x for 4 months
After 4 months, A invested $2000 more and B invested $7000 more each month for the remaining 8 months.
For the next 8 months: A's investment = (18x + 2000) for 8 months B's investment = (7x + 7000) for 8 months
Total investment-time for A = 18x × 4 + (18x + 2000) × 8 = 72x + 144x + 16000 = 216x + 16000
Total investment-time for B = 7x × 4 + (7x + 7000) × 8 = 28x + 56x + 56000 = 84x + 56000
Given that profit is distributed in ratio 2:1, the investment ratio should also be 2:1
So: (216x + 16000)/(84x + 56000) = 2/1
216x + 16000 = 2(84x + 56000)
216x + 16000 = 168x + 112000
216x - 168x = 112000 - 16000
48x = 96000
x = 2000
Therefore:
A's initial investment = 18x = 18 × 2000 = $36000
B's initial investment = 7x = 7 × 2000 = $14000
Total initial investment = $36000 + $14000 = $50000
The answer is A) $50,000
For the first 4 months:
A's investment = 18x for 4 months
B's investment = 7x for 4 months
After 4 months, A invested $2000 more and B invested $7000 more each month for the remaining 8 months.
For the next 8 months: A's investment = (18x + 2000) for 8 months B's investment = (7x + 7000) for 8 months
Total investment-time for A = 18x × 4 + (18x + 2000) × 8 = 72x + 144x + 16000 = 216x + 16000
Total investment-time for B = 7x × 4 + (7x + 7000) × 8 = 28x + 56x + 56000 = 84x + 56000
Given that profit is distributed in ratio 2:1, the investment ratio should also be 2:1
So: (216x + 16000)/(84x + 56000) = 2/1
216x + 16000 = 2(84x + 56000)
216x + 16000 = 168x + 112000
216x - 168x = 112000 - 16000
48x = 96000
x = 2000
Therefore:
A's initial investment = 18x = 18 × 2000 = $36000
B's initial investment = 7x = 7 × 2000 = $14000
Total initial investment = $36000 + $14000 = $50000
The answer is A) $50,000
Shivam2027
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27 Feb 2026, 03:16
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a very great qn and im glad to see people doing this because it helps us all
Mizan42
