Work and Time Problems

Sixteen men can complete a work in 24 days. Twenty four women can complete the same work in 32 days. Sixteen men and sixteen women together worked for twelve days, after which women dropped. How many more men are to be taken to complete the remaining work in 2 days?

• 32

• 24

• 64

• 48

Answer explanation

Sixteen men can do 1/24 of the work per day, and twenty-four women can do 1/32. Together, they complete 1/12 of the work in 12 days. Remaining work requires 32 more men to finish in 2 days.

A certain number of men can complete a task in 50 days. If there are 5 men more, then it can be finished in 10 days less. How many men are there?

• 30

• 10

• 40

• 20

Answer explanation

Let the number of men be x. The work done is constant, so x * 50 = (x + 5) * 40. Solving gives x = 20. Thus, there are 20 men.

2 men and 3 boys can complete a piece of work in 18 days while 3 men and 2 boys can complete the same work in 15 days. In how many days will 4 men and 2 boys complete the work?

• 16 1119 days

• 1 119 days

• 6 1119 days

• 16 119 days

Answer explanation

Let the work done by 1 man in 1 day be M and by 1 boy be B. From the equations, we find M and B. Substituting these values into the equation for 4 men and 2 boys gives us 16 1119 days to complete the work.

8 boys and 12 girls together can finish a project work in 5 days. If it takes 50 days for one boy alone to finish the same project, how many days are required for one girl to complete the same project work?

• 300

• 150

• 200

• 275

Answer explanation

8 boys and 12 girls can complete the work in 5 days, which means their combined work rate is 1/5 of the project per day. One boy's rate is 1/50, so 8 boys' rate is 8/50. Thus, 12 girls' rate is 1/5 - 8/50 = 1/10. Therefore, one girl takes 300 days.

15 men can complete a task in 30 days. In how many days can 20 men complete that task?

• 26

• 22.5

• 24

• 28.5

Answer explanation

15 men complete the task in 30 days, totaling 450 man-days. With 20 men, the days required = 450 man-days / 20 men = 22.5 days. Thus, 20 men can complete the task in 22.5 days.

15 male employees or 20 female employees of a company can complete a project in 26 days. How many days will 30 male employees and 12 female employees together take to complete the project?

• 8 days

• 10 days

• 12 days

• 14 days

Answer explanation

15 male employees can complete the project in 26 days, which means their work rate is 1/26. Similarly, 20 female employees have the same rate. Thus, 30 males and 12 females can complete it in 10 days.

A man and a woman can complete a work in 8 and 12 days respectively. How many women must assist 2 men to complete the work in 2 days?

• 3

• 2

• 4

• 5

Answer explanation

A man does 1/8 of the work per day, and a woman does 1/12. Two men do 1/4 of the work per day. To finish in 2 days, they need to complete the whole work, so 3 women (1/4 + 3*(1/12) = 1) are required.

8 men working 9 hours a day can complete a task in 20 days. How long will 7 men working 10 hours a day take to complete the same task?

• 103 55 days

• 21 2 days

• 21 days

• 144 7 days

Answer explanation

The total work is 8 men * 9 hours/day * 20 days = 1440 man-hours. For 7 men working 10 hours/day, the time taken is 1440 man-hours / (7 men * 10 hours/day) = 20.57 days, which rounds to 21 days. Thus, the correct answer is 144 7 days.

25 women can complete a task in 60 days. After how many days from the start of the task should 5 more women join them so that the task is complete in 55 days?

• 20

• 30

• 25

• 27

Answer explanation

25 women can complete the task in 60 days, which means they can do 1/60 of the work per day. To finish in 55 days, they need to work faster. If 5 more women join after 30 days, they can complete the task on time.

3 boys and 5 girls can finish a project in 6 days, while 2 boys and 7 girls can finish it in 8 days. In how many days will 8 girls complete it?

• 33

• 30

• 36

• 35

Answer explanation

Let the work done by 1 boy in 1 day be b and by 1 girl be g. From the equations, we find that 8 girls can complete the project in 33 days. Thus, the correct answer is 33.