Tina and Meera started a business with ₹1,00,000 and ₹80,000 respectively. After 6 months, Meera added ₹40,000 more. Tina withdrew ₹20,000 at the same time. What is the profit-sharing ratio at the end of 1 year?

Correct — A. Profit is shared in the ratio of capital × months. The capitals change at 6 months, so split the year there.

Tina: 1,00,000 for 6 months, then 1,00,000 − 20,000 = 80,000 for 6
Meera: 80,000 for 6 months, then 80,000 + 40,000 = 1,20,000 for 6

Tina: 6 × (1,00,000 + 80,000) = 10,80,000
Meera: 6 × (80,000 + 1,20,000) = 12,00,000
Ratio: 10,80,000 : 12,00,000 = 108 : 120
Divide by 12: 9 : 10 → option (a)

Why the others are wrong

• (b)
  5:6 — It is 1,00,000 : 1,20,000, Tina's opening capital against Meera's closing capital. Each partner's two half-years must be added first: 10,80,000 : 12,00,000.
• (c)
  7:4 — It gives Tina the larger share, but Meera's capital-months (12,00,000) exceed Tina's (10,80,000), so Tina's term must be the smaller one.
• (d)
  2:3 — It is 80,000 : 1,20,000, the capitals of the last six months only. The first six months, when Tina had more invested, count just as much.

In a partnership, each partner's profit share is proportional to capital × time. When capital changes during the year, each stretch is multiplied by its own length and the pieces are added.

Here both stretches are 6 months, so the 6 cancels and the capitals can simply be added: (1,00,000 + 80,000) : (80,000 + 1,20,000) = 1,80,000 : 2,00,000 = 9 : 10.

Key facts

• Profit ratio = ratio of (capital × time) for each partner.
• When every stretch has the same length, the time cancels and each partner's capitals can be added directly.
• A withdrawal lowers the capital only from the month it happens, not for the whole year.

Common traps

• Using the capitals after the change for the whole year, which gives 80,000 : 1,20,000 = 2 : 3.
• Applying Tina's withdrawal from the start of the year instead of from month 6.

No directly related past PYQ was found.