Arvind started a business by investing ₹80,000. After 4 months, Bhavin joined with ₹1,20,000. At the end of 8 months from the start, Chandan joined with ₹1,60,000. If the total profit is ₹1,05,000 at the end of the year, find the share of Chandan.

Correct — D. Profit is shared in the ratio of capital × months.

Arvind, 12 months: 80,000 × 12 = 9,60,000
Bhavin joins after 4, so 8 months: 1,20,000 × 8 = 9,60,000
Chandan joins after 8, so 4 months: 1,60,000 × 4 = 6,40,000

Divide by 3,20,000: ratio = 3 : 3 : 2, total 8 parts
Chandan = 2⁄8 × 1,05,000 = ₹26,250 → option (d)

Why the others are wrong

• (a)
  ₹26,500 — Chandan's 2 of 8 parts is exactly one quarter, so his share × 4 must return the profit. ₹26,500 × 4 = ₹1,06,000, which is ₹1,000 too much.
• (b)
  ₹26,000 — ₹26,000 × 4 = ₹1,04,000, ₹1,000 short of the ₹1,05,000 profit. A one-quarter share has to multiply back to the whole.
• (c)
  ₹26,200 — ₹26,200 × 4 = ₹1,04,800, still ₹200 short of ₹1,05,000. Close is not enough when the share is an exact quarter.

In a partnership the profit is split in the ratio of capital × time, the capital-months each partner puts in.

A late joiner counts only from the month of joining to the year's end. 'After 4 months' leaves 12 − 4 = 8 months. 'At the end of 8 months' leaves 12 − 8 = 4.

Once the capital-months are a ratio, each share is that fraction of the total profit.

Key facts

• Profit share is proportional to capital × months invested.
• A partner who joins after k months of a 12-month year is invested for 12 − k months.
• Here the capital-months are 9,60,000 : 9,60,000 : 6,40,000 = 3 : 3 : 2.

Common traps

• Giving Chandan 8 months because 8 is the number in his sentence: he joins at the end of month 8 and stays 4.
• Splitting by capital alone, 2 : 3 : 4, which hands Chandan 4⁄9 of the profit, about ₹46,667.

No directly related past PYQ was found.