Joint business with unequal capitals and times: A and B start a business. A’s capital is thrice B’s capital, and A keeps it invested for twice B’s time. If B’s profit share is ₹ 6000, what is 20% of the total profit?

Introduction / Context:
In partnership problems, the profit share of each partner is proportional to the product of capital and time. Here, A’s capital is larger and invested longer, while we are given B’s final share. From this, we reconstruct the total and then find 20% of it.

Given Data / Assumptions:

• A’s capital = 3 × B’s capital.
• A’s time = 2 × B’s time.
• Profit share ratio A : B = (3 × 2) : 1 = 6 : 1.
• B’s profit = ₹ 6000 (i.e., 1 part).

Concept / Approach:
If A : B = 6 : 1, then total parts = 7. Hence the total profit equals 7 times B’s share. Then take 20% of that total as required by the question.

Step-by-Step Solution:
Total profit = 7 × ₹ 6000 = ₹ 42000.Required = 20% of ₹ 42000 = 0.20 * 42000 = ₹ 8400.

Verification / Alternative check:
Check the internal split: A gets 6 × 6000 = ₹ 36000, B gets ₹ 6000; total ₹ 42000. Twenty percent of that is indeed ₹ 8400.

Why Other Options Are Wrong:

• ₹ 5000, ₹ 3500, and ₹ 4500 are not 20% of ₹ 42000; thus they do not fit the derived total.

Common Pitfalls:

• Treating capitals alone as the basis, ignoring the time factor.
• Multiplying B’s share by 20% directly without computing the total profit first.

Final Answer:
₹ 8400