Aptitude – Time and work

(6) M and N can do a piece of work in 24 days. N and O in 30 days and O and M in 40 days. In how many days can M do the work alone?

• (a) 48 days
• (b) 60 days
• (c) 72 days
• (d) 90 days

Correct Answer: (a) 48 days
\frac{1}{M} + \frac{1}{N} = \frac{1}{24}, \frac{1}{N} + \frac{1}{O} = \frac{1}{30}, \frac{1}{O} + \frac{1}{M} = \frac{1}{40}
M's time = \frac{2}{\frac{1}{24} + \frac{1}{40} - \frac{1}{30}} = 48 \text{ days}

(7) A and B can complete a work in 10 days. B and C in 12 days and C and A in 15 days. How long will B take to do it alone?

• (a) 24 days
• (b) 30 days
• (c) 20 days
• (d) 18 days

Correct Answer: (c) 20 days
\frac{1}{A} + \frac{1}{B} = \frac{1}{10}, \frac{1}{B} + \frac{1}{C} = \frac{1}{12}, \frac{1}{C} + \frac{1}{A} = \frac{1}{15}
B's time = \frac{2}{\frac{1}{10} + \frac{1}{12} - \frac{1}{15}} = 20 \text{ days}

(8) If 20 men can build a wall in 40 days, how many men are required to do the same in 30 days?

• (a) 25 men
• (b) 27 men
• (c) 30 men
• (d) 35 men

Correct Answer: (b) 27 men
Men \times Days = Constant
20 \times 40 = N \times 30
N = \frac{20 \times 40}{30} = 27 \text{ men}

(9) A, B, and C can do a job in 6 days, 9 days, and 12 days, respectively. How long will they take to do it together?

• (a) 3 days
• (b) 4 days
• (c) 5 days
• (d) 6 days

Correct Answer: (a) 3 days
\frac{1}{A} + \frac{1}{B} + \frac{1}{C} = \frac{1}{6} + \frac{1}{9} + \frac{1}{12}
Total time = \frac{1}{\frac{1}{6} + \frac{1}{9} + \frac{1}{12}} = 3 \text{ days}

(10) A machine A can print one lakh books in 8 hours, machine B can print the same in 10 hours, while machine C can print them in 12 hours. All the machines are started at 9 A.M. At what time will they complete printing one lakh books together?

• (a) 2:24 PM
• (b) 3:20 PM
• (c) 4:10 PM
• (d) 5:00 PM

Correct Answer: (b) 3:20 PM
Total time = \frac{1}{\frac{1}{8} + \frac{1}{10} + \frac{1}{12}}
= \frac{1}{\frac{15}{120}} = 8 \text{ hours}
Completion time = 9 \text{ AM} + 8 \text{ hours} = 3:20 \text{ PM}