A and B undertake to complete a piece of work for Rs. 600. A alone can complete it in 4 days while B alone can complete it in 6 days. With the help of C, they finish the work in 2 days. Find the share of C in the payment received.

Correct option is A

Given:
Amount of work = ₹600
Time taken by A alone = 4 days
Time taken by B alone = 6 days
Time taken by A, B, and C together = 2 days

Formula Used:
Efficiency = Total Work ÷ Time

Solution:
​$$\text{Let the total work be the least common multiple (LCM) of 4, 6, and 2:} \\\ \\\text{Total Work} = 12 \, \text{units}.\\\ \\\text{Efficiency of A:} \\\ \\\text{Efficiency of A} = \frac{12}{4} = 3 \, \text{units/day}. \\\ \\\text{Efficiency of B:}\\\ \\\text{Efficiency of B} = \frac{12}{6} = 2 \, \text{units/day}.\\\ \\\text{Efficiency of A, B, and C together:} \\\ \\\text{Efficiency of (A + B + C)} = \frac{12}{2} = 6 \, \text{units/day}. \\\ \\\text{Efficiency of C:} \\\ \\\text{Efficiency of C} = \text{Efficiency of (A + B + C)} - \text{Efficiency of (A + B)}. \\\ \\\text{Substituting values:} \\\ \\\text{Efficiency of C} = 6 - (3 + 2) = 1 \, \text{unit/day}.\\\ \\\text{Share of C in ₹600:} \\\ \\\text{Total work done} = 12 \, \text{units}, \quad \text{C's contribution} = 1 \, \text{unit/day} \times 2 \, \text{days} = 2 \, \text{units}.\\\ \\\text{Share of C} = ₹600 \times \frac{2}{12} = ₹100. \\\ \\$$​​