In a partnership firm, A invests 1/6th of the total investment for 1/6th of the tenure. B invests 1/3rd of the total investment for 1/3rd of the tenure while C invests the remaining part for the full duration. Out of total profit of ₹46,00,000, what shall be C's share?

Correct — D, ₹36,00,000. Profit in a partnership follows capital multiplied by time. Let the total investment be I and the tenure T. A contributes (I/6) × (T/6) = IT/36. B contributes (I/3) × (T/3) = IT/9, which is 4IT/36. C's share of the money is the remainder, 1 − 1/6 − 1/3 = 1/2, invested for the whole period: (I/2) × T = 18IT/36. The three are therefore in the ratio 1 : 4 : 18, totalling 23 parts. One part is 46,00,000 ÷ 23 = ₹2,00,000, so C's 18 parts come to ₹36,00,000.

• (a)₹30,00,000 — ₹30,00,000 is 15 parts of 23, which no combination of the given fractions produces. C's capital-months are 18 parts.
• (b)₹32,00,000 — This would follow from crediting C with half the investment for half the tenure rather than the full duration.
• (c)₹34,00,000 — ₹34,00,000 is 17 parts. It appears if B's contribution is counted as 1/3 × 1/3 of the total in one place and as 1/3 alone in another.

When partners invest for unequal periods, profit is divided in the ratio of their capital multiplied by time, a product often called capital-months. Equal capitals held for unequal periods, or unequal capitals held for equal periods, are both special cases of the same rule. The remaining partner's share of the capital is whatever the named fractions leave.

The arithmetic is easy once every contribution is written over a common denominator of 36. A gives 1, B gives 4, C gives 18. The step candidates miss is C's capital: the stem never states it, and it has to be recovered as 1 − 1/6 − 1/3 = 1/2. The other check is that the parts must divide the profit exactly, and 46,00,000 ÷ 23 = 2,00,000 confirms the ratio has been built correctly.

• Profit share is proportional to capital × time invested.
• A: (1/6) × (1/6) = 1/36. B: (1/3) × (1/3) = 4/36. C: (1/2) × 1 = 18/36.
• The ratio A : B : C is 1 : 4 : 18, so the profit divides into 23 parts.
• One part is ₹46,00,000 ÷ 23 = ₹2,00,000, and C's 18 parts are ₹36,00,000.
• C's capital is not stated and must be found as the remainder after A's sixth and B's third.

• Sharing the profit in the ratio of capital alone and ignoring the time each stayed in.
• Taking C's investment as 1/2 for 1/2 the tenure instead of the full duration.
• Failing to compute C's capital as the leftover fraction.

A partnership item that hides one partner's capital behind a subtraction and pays for the discipline of writing capital and time as a single product.

No directly related past PYQ was found.

• practice — not a real PYQ

  A invests ₹5,000 for 12 months and B invests ₹10,000 for 6 months. In what ratio is the profit divided?

  • (a)1 : 1
  • (b)1 : 2
  • (c)2 : 1
  • (d)5 : 6

  Answer(a) 1 : 1 — capital-months are 60,000 for each, so the profit is shared equally.

• practice — not a real PYQ

  X, Y and Z invest in the ratio 2 : 3 : 5 for the same period. Out of a profit of ₹40,000, Z receives

  • (a)₹8,000
  • (b)₹12,000
  • (c)₹18,000
  • (d)₹20,000

  Answer(d) ₹20,000 — Z has 5 of the 10 parts, that is half the profit.