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 P, Q and R invested some amount to start a business. P invest 500 for 12 months, Q invest 600 for some months and R invested 540 more than 2 months invested by Q.At the end of the year total profit earned is Rs.2200 while Q received Rs.480 then Q invested foe how many months ?

  • a)
    7 months

  • b)
    9months

  • c)
    10 months

  • d)
    8 months

  • e)
    None of these

Correct answer is option 'D'. Can you explain this answer?
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P, Q and R invested some amount to start a business. P invest 500 for ...
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P, Q and R invested some amount to start a business. P invest 500 for ...
Given:
- P invests Rs.500 for 12 months.
- Q invests Rs.600 for some months.
- R invests Rs.540 more than twice the number of months invested by Q.
- Total profit earned is Rs.2200.
- Q receives Rs.480.

To find:
- The number of months Q invested.

Assumptions:
- The profit is divided among the partners in proportion to their investments.

Let's solve the problem step by step:

Step 1:
Let's assume Q invests for x months.
- P invests for 12 months.
- R invests for 2x + 540 months.

Step 2:
Now, we need to calculate the ratio of their investments.
- P's investment = Rs.500 * 12 = Rs.6000
- Q's investment = Rs.600 * x = Rs.600x
- R's investment = Rs.(2x + 540) * 600 = Rs.(1200x + 324000)

Step 3:
Since the profit is divided in proportion to their investments, we can calculate the ratio of their profits.
- P's profit = (6000 / total investment) * total profit = (6000 / (6000 + 600x + 1200x + 324000)) * 2200
- Q's profit = (600x / (6000 + 600x + 1200x + 324000)) * 2200
- R's profit = ((1200x + 324000) / (6000 + 600x + 1200x + 324000)) * 2200

Step 4:
We know that Q's profit is Rs.480.
- (600x / (6000 + 600x + 1200x + 324000)) * 2200 = 480

Step 5:
Solve the equation to find the value of x.
- 600x = 480 * (6000 + 600x + 1200x + 324000)
- 600x = 480 * (1800x + 330000)
- 600x = 864000x + 158400000
- 864000x - 600x = 158400000
- 863400x = 158400000
- x = 158400000 / 863400
- x ≈ 183.33

Step 6:
Since the investment period cannot be in decimal, we need to round off the value of x.
- Rounded off value of x is 183.

Step 7:
Therefore, Q invested for 183 months, which is approximately equal to 8 months.

Hence, the correct answer is option D) 8 months.
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