Aptitude – Time and work

(15) 20 workers can complete a project in 30 days. After 10 days, 10 workers left. In how many more days will the remaining workers complete the project?

• (a) 25 days
• (b) 30 days
• (c) 20 days
• (d) 35 days

Answer

Correct Answer: (b) 30 days
Work done in 10 days = 10 \times \frac{20}{30} = \frac{2}{3}
Remaining work = 1 - \frac{2}{3} = \frac{1}{3}
Time for 10 workers to complete remaining work = \frac{\frac{1}{3}}{\frac{10}{30}} = 10 \text{ days}

(16) R, S, and T can do a piece of work in 20 days, 30 days, and 60 days respectively. They start the work together, but R leaves after 5 days and S leaves 3 days before the work is finished. In how many days will the work be completed?

• (a) 12 days
• (b) 15 days
• (c) 18 days
• (d) 20 days

Answer

Correct Answer: (b) 15 days
R's rate = \frac{1}{20}, S's rate = \frac{1}{30}, T's rate = \frac{1}{60}
Combined rate for first 5 days = \frac{1}{20} + \frac{1}{30} + \frac{1}{60}
Work done in first 5 days = 5 \times \left(\frac{1}{20} + \frac{1}{30} + \frac{1}{60}\right)
Remaining work after 5 days = 1 - \text{[Work done in first 5 days]}
S and T's rate for next (t-8) days = \frac{1}{30} + \frac{1}{60}
T's rate for last 3 days = \frac{1}{60}
\text{Solve for t}