Multiple choice

A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After two months, A withdraws half of his capital. At the end of year, a profit of Rs. 378 is divided among them. What is B's share (in Rs.)?

  1. 129

  2. 144

  3. 156

  4. 168

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Ratio 1/2:1/3:1/4 simplifies to 6:4:3. Let capitals be 6x, 4x, 3x. A's effective capital is (6x*2 + 3x*10) = 42x. B's is 4x*12 = 48x. C's is 3x*12 = 36x. Ratio is 42:48:36 or 7:8:6. Total parts = 21. B's share = (8/21)*378 = 144.

AI explanation

Multiply the given ratio one-half to one-third to one-fourth by the lowest common multiple of 2, 3 and 4, which is 12, to get an initial investment ratio of 6 to 4 to 3. After two months, A withdraws half his capital, making his effective capital 6 units for 2 months plus 3 units for 10 months, equaling 42 unit-months. B and C keep their capital for the full year, yielding 48 unit-months for B and 36 unit-months for C, so the new ratio is 42 to 48 to 36, which simplifies to 7 to 8 to 6. Since the total of 21 parts represents 378, one part is 18, and B's share of 8 parts is 144.

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