Question

2 men and 5 boys can finish a piece of work in 4 days, while 3 men and 6 boys can finish it in 3 days. The time taken by one man alone to finish the work is:

• A. 20 days
• B. 18 days
• C. 14 days
• D. 16 days

Hint:

When solving work problems, express total work as 1 unit, determine individual work rates, and use simultaneous equations to solve for unknowns.

Answer 1

The Correct Option is B

Let: - Work done by 1 man per day = \( M \) - Work done by 1 boy per day = \( B \) Given: 1. 2 men and 5 boys finish the work in 4 days: \[ 4(2M + 5B) = 1 \] \[ 2M + 5B = \frac{1}{4} \] 2. 3 men and 6 boys finish the work in 3 days: \[ 3(3M + 6B) = 1 \] \[ 3M + 6B = \frac{1}{3} \] Solving: Multiply the first equation by 3 and the second by 2: \[ 6M + 15B = \frac{3}{4} \] \[ 6M + 12B = \frac{2}{3} \] Subtracting: \[ (6M + 15B) - (6M + 12B) = \frac{3}{4} - \frac{2}{3} \] \[ 3B = \frac{9}{12} - \frac{8}{12} = \frac{1}{12} \] \[ B = \frac{1}{36} \] Substituting into \( 2M + 5B = \frac{1}{4} \): \[ 2M + \frac{5}{36} = \frac{1}{4} \] \[ 2M = \frac{9}{36} - \frac{5}{36} = \frac{4}{36} \] \[ M = \frac{1}{18} \]
Thus, one man alone will take: \[ \frac{1}{\frac{1}{18}} = 18 \text{ days} \]
Thus, the correct answer is 18 days.