Question

A and B undertake to do a piece of work for ₹1200. A alone can do it in 12 days while B alone can do it in 16 days. With the help of C, they finish it in 6 days. Then identify the correct statements:
A. A's share = ₹640
B. B's share = ₹450
C. C's share = ₹150
D. C's one day's work = 1/40

• A. A and B Only
• B. B and C Only
• C. A, B and D Only
• D. C and D Only

Hint:

Always calculate the total efficiency of the group first. If A and B take most of the efficiency (7 out of 8 parts), C's share should be the smallest (1/8th of 1200).

Answer 1

The Correct Option is B

Concept: When a group of people works together for a total wage, the money is distributed in the ratio of the total work done by each individual. If they work for the same number of days, the money is shared in the ratio of their daily efficiencies.

Step 1: Find individual efficiencies.
Let total work $= 48$ units (LCM of 12, 16, 6). Efficiency of A $= 48 / 12 = 4$ units/day. Efficiency of B $= 48 / 16 = 3$ units/day. Efficiency of (A+B+C) $= 48 / 6 = 8$ units/day. Efficiency of C $= 8 - (4 + 3) = 1$ unit/day.

Step 2: Evaluate Statement D.
C's one day's work (efficiency) $= 1 / 48$ of the total work.
Statement D says $1/40$, so D is incorrect.

Step 3: Distribute the wages (₹1200).
The ratio of work done is the ratio of efficiencies: $4 : 3 : 1$. Total parts $= 4 + 3 + 1 = 8$ parts. Value of 1 part $= 1200 / 8 = ₹150$.
• A's share: $4 \times 150 = ₹600$ (Statement A says ₹640, so A is incorrect).
• B's share: $3 \times 150 = ₹450$ (Statement B is Correct).
• C's share: $1 \times 150 = ₹150$ (Statement C is Correct). Therefore, only B and C are correct.