Partnership

Step 1: Calculate individual investments and durations.

• A's investment:
  Amount = ₹10,000
  Duration = 12 months
  Total contribution = ₹10,000 × 12 = ₹120,000
• B's investment:
  Amount = ₹18,000
  Duration = 6 months (joined at the start, left after 6 months)
  Total contribution = ₹18,000 × 6 = ₹108,000
• C's investment:
  Amount = ₹12,000
  Duration = 8 months (joined after 4 months)
  Total contribution = ₹12,000 × 8 = ₹96,000

Step 2: Calculate the ratio of their contributions.

Total contribution ratios:
A : B : C = ₹120,000 : ₹108,000 : ₹96,000.

• Simplifying to a smaller ratio:
  Divide each by 12,000:
  A : B : C = 10 : 9 : 8

Step 3: Determine A's share of the profit and calculate the total profit.

According to the problem, A's share is ₹7,500. Use this share to find out the total profit.

Let the total profit be X.

Then, A's share of the profit is given by the ratio part:
A's portion of profit = (10/(10+9+8)) × X = (10/27) × X = ₹7,500

Therefore:
X = ₹7,500 × (27/10) = ₹7,500 × 2.7 = ₹20,250

Conclusion: Thus, the total profit earned is ₹20,250.