Aptitude – Time and work

(11) A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work?

• (a) 27 days
• (b) 30 days
• (c) 36 days
• (d) 54 days

Correct Answer: (a) 27 days
A's 1 day work = 2 \times B's 1 day work
A's time = \frac{18}{3} = 6 \text{ days}

(12) A and B can complete a piece of work in 10 days and 15 days respectively. They start working together but B leaves after 2 days. In how many days will A complete the remaining work?

• (a) 8 days
• (b) 9 days
• (c) 10 days
• (d) 12 days

Answer

Correct Answer: (b) 9 days
A's rate = \frac{1}{10}, B's rate = \frac{1}{15}
Work done in 2 days = 2 \times \left(\frac{1}{10} + \frac{1}{15}\right) = \frac{1}{3}
Remaining work = 1 - \frac{1}{3} = \frac{2}{3}
Time for A to complete remaining work = \frac{\frac{2}{3}}{\frac{1}{10}} = 9 \text{ days}

(13) If 6 workers can build a wall in 8 days, how many workers are needed to build it in 4 days?

• (a) 12 workers
• (b) 10 workers
• (c) 8 workers
• (d) 15 workers

Answer

Correct Answer: (a) 12 workers
Workers \times Days = Constant
6 \times 8 = W \times 4
W = \frac{6 \times 8}{4} = 12 \text{ workers}

(14) L and M can do a work in 12 days and 18 days respectively. They start the work together, but L leaves 3 days before the work is completed. In how many days is the work completed?

• (a) 10 days
• (b) 10.5 days
• (c) 11 days
• (d) 9 days

Answer

Correct Answer: (b) 10.5 days
L's rate = \frac{1}{12}, M's rate = \frac{1}{18}
Combined rate = \frac{1}{12} + \frac{1}{18} = \frac{5}{36}
Work done in (t-3) days = (t-3) \times \frac{5}{36}
M's work in last 3 days = 3 \times \frac{1}{18}
(t-3) \times \frac{5}{36} + 3 \times \frac{1}{18} = 1
t = 10.5 \text{ days}