A and B started a business by investing ₹10,000 and ₹18,000 respectively. Their investments remained for different durations, which will affect their profit shares. Let's calculate the weighted investments for each partner.
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.