A and B are partners in a business. A invests ₹20,000 for a period of 2 years. B invests ₹30,000 for a period of 3 years. If A's share of the total profit is ₹4,000, what is B's share of the profit?

Correct — A.
Rule: profit is shared in the ratio of capital × time.

A: 20,000 × 2 = 40,000
B: 30,000 × 3 = 90,000
Ratio = 40,000 : 90,000 = 4 : 9

A's 4 parts = ₹4,000, so 1 part = ₹1,000
B's 9 parts = 9 × 1,000 = ₹9,000 → option (a).

Why the others are wrong

• (b)
  ₹4,000 — ₹4,000 splits the profit equally, as if both put in the same money for the same time. B's capital × time (90,000) is more than double A's (40,000).
• (c)
  ₹5,000 — ₹5,000 makes the split 4 : 5. The capital-time products give 4 : 9, so B's share must be more than twice A's ₹4,000.
• (d)
  ₹7,000 — ₹7,000 makes the split 4 : 7, still under twice A's share. B's product is 2.25 times A's, so B gets 2.25 × ₹4,000.

In a partnership, profit is divided in the ratio of each partner's capital × time. A partner who puts in more money, or keeps it in longer, earns proportionally more.

Work out each product, reduce the ratio, find one part from the share you are given, then scale up to the share you want.

Key facts

• Profit ratio = capital × time for each partner.
• If the times are equal, the ratio is just the ratio of capitals.
• One part = the known share ÷ its number in the ratio.

Common traps

• Splitting by capital alone (2 : 3), which gives ₹6,000: not an option, and a sign that time was left out
• Reporting the total profit (13 parts = ₹13,000) instead of B's share

No directly related past PYQ was found.