Aptitude – Time and work

Aptitude – Time and work

(1) A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

• (a) Rs. 375
• (b) Rs. 400
• (c) Rs. 600
• (d) Rs. 800

Answer

Correct Answer: (b) Rs. 400
C's 1 day's work = \left(\frac{1}{3}\right) - \left[\frac{1}{6} + \frac{1}{8}\right] = \frac{1}{3} - \frac{7}{24} = \frac{1}{24}
A's wages : B's wages : C's wages = \frac{1}{6} : \frac{1}{8} : \frac{1}{24}
= 4:3:1
C's share (for 3 days) = 3 \times \left(\frac{1}{24}\right) \times 3200 = Rs 400

(2) Worker X can complete a task in 15 days. Worker Y is 50% more efficient than X. How long will it take for Y to complete the same task?

• (a) 10 days
• (b) 12 days
• (c) 20 days
• (d) 7.5 days

Answer

Correct Answer: (a) 10 days
Y's efficiency = 1.5 \times X's efficiency
Y's time = \frac{X's time}{1.5} = \frac{15}{1.5} = 10 \text{ days}

(3) P and Q can do a job in 20 days together. P is 25% more efficient than Q. In how many days can P complete the job alone?

• (a) 24 days
• (b) 32 days
• (c) 30 days
• (d) 35 days

Answer

Correct Answer: (c) 30 days
P's efficiency = 1.25 \times Q's efficiency
\frac{1}{P's time} = \frac{1.25}{20}
P's time = \frac{20}{1.25} = 16 \text{ days}

(4) If 10 men or 15 women can complete a work in 60 days, how many days will 5 men and 6 women take to complete the same work?

• (a) 100 days
• (b) 60 days
• (c) 80 days
• (d) 120 days

Answer

Correct Answer: (b) 60 days
1 \text{ man's 1 day work} = \frac{1}{600}
1 \text{ woman's 1 day work} = \frac{1}{900}
5 \text{ men and 6 women's 1 day work} = 5 \times \frac{1}{600} + 6 \times \frac{1}{900} = \frac{1}{60}
Total time = \frac{1}{\frac{1}{60}} = 60 \text{ days}

(5) R and S together can finish a piece of work in 12 days. S and T together can do it in 15 days, while T and R can do it in 20 days. How long will R take to do it alone?

• (a) 30 days
• (b) 24 days
• (c) 36 days
• (d) 40 days

Answer

Correct Answer: (b) 24 days
\frac{1}{R} + \frac{1}{S} = \frac{1}{12}, \frac{1}{S} + \frac{1}{T} = \frac{1}{15}, \frac{1}{T} + \frac{1}{R} = \frac{1}{20}
\frac{2}{R} + \frac{2}{S} + \frac{2}{T} = \frac{1}{12} + \frac{1}{15} + \frac{1}{20}
R's time = \frac{2}{\frac{1}{12} + \frac{1}{15} + \frac{1}{20} - \frac{1}{R}} = 24 \text{ days}