A invests ₹25,000 for 12 months, B invests ₹50,000 for 6 months. What is A’s share of ₹30,000 profit?

Correct — C. Profit is shared in the ratio of capital × time.

A: 25,000 × 12 = 3,00,000
B: 50,000 × 6 = 3,00,000

Ratio A : B = 3,00,000 : 3,00,000 = 1 : 1
A's share = 30,000 × 1⁄2 = ₹15,000 → option (c)

Why the others are wrong

• (a)
  ₹10,000 — ₹10,000 splits by capital alone, 25,000 : 50,000 = 1 : 2. That ignores time: A's money stayed 12 months against B's 6, which evens the products.
• (b)
  ₹12,000 — ₹12,000 is 2⁄5 of the profit, a 2 : 3 split. Neither capital nor time gives 2 : 3 here, and the products of 3,00,000 each give 1 : 1.
• (d)
  ₹18,000 — ₹18,000 is 3⁄5 of the profit, which would need A's capital × time to exceed B's. Both products are 3,00,000, so A gets exactly half.

In a partnership, profit is divided in the ratio of each partner's capital × time, the investment measured in rupee-months.

Here A puts in half the money for double the time, so the two products are equal. Equal products mean an equal split, whatever the rupee amounts.

Key facts

• Each partner's profit share is proportional to capital × time.
• 25,000 × 12 = 50,000 × 6 = 3,00,000.
• Equal capital × time products give each partner half the profit.

Common traps

• Splitting by capital alone (1 : 2) because the months look like extra information.
• Splitting by months alone (12 : 6 = 2 : 1), which would give A ₹20,000.

No directly related past PYQ was found.