Question

If 40 boys can do a piece of work in 18 days working 6 hours per day, how many more boys are required to do the same work in 12 days working 4 hours per day?

• A. 50
• B. 56
• C. 40
• D. 45

Hint:

Total work = workers × days × hours/day; keep total work constant while changing variables to find unknown.

Answer 1

The Correct Option is A

The total work is calculated in boy-hours: \[\text{Work} = \text{number of boys} \times \text{days} \times \text{hours/day} = 40 \times 18 \times 6 = 4320 \text{ boy-hours}\] Let $x$ represent the number of additional boys required, making the total number of boys $40 + x$. With the adjusted work schedule of 12 days, working 4 hours/day, the equation is: \[(40 + x) \times 12 \times 4 = 4320\] \[(40 + x) \times 48 = 4320 \implies 40 + x = \frac{4320}{48} = 90\] \[x = 90 - 40 = 50\]