# Quantitative Aptitude : Time and Work Practice Problems with Explanations

### TIME AND WORK

• If A can do a piece of work in n days, work done by A in 1 day = 1/n.
• If A does 1/n work in a day, A can finish the work in n days.
• If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do W2 work in D2 days working H2 hours per day (where all men work at the same rate), then,
• M1 D1 H1W2 = M2 D2 H2 W1
• If A can do a piece of work in p days and B can do the same in q days, A and B together can finish it in pq / (p+q) days.
• If A is thrice as good as B in work, then
• Ratio of work done by A and B = 3 : 1
• Ratio of time taken to finish a work by A and B = 1 : 3

### Practice Problems :

1. A and B together can complete a particular task in 4 days. If A alone can complete the same task in 12 days, how many days will B take to complete the task if he works alone ?
1. 9 days
2. 7 days
3. 5 days
4. 3 days
5. None of these
2. A and B together can complete a particular task in 8 days. If B alone can complete the same task in 10 days, how many days will A take to complete the task if he works alone ?
1. 28
2. 36
3.  40
4. 32
5. None of these
3. A and B together can complete a particular task in 6 days. If A alone can complete the same task in 10 days, how many days will B take to complete the task if he works alone ?
1. 15
2.  16
3. 14
4. 12
5. None of these
4. A and B together can complete a particular task in 4 days. If A alone can complete the same task in 6 days, how many days will B take to complete the task if he work alone ?
1. 8
2. 17
3. 14
4. 12
5. None of these
5. Yesterday Priti typed an essay of 5000 words at the speed of 60 words per minute. Today she typed the same essay faster and her speed was 15 % more than yesterday. What is the approximate difference in the time she took to type yesterday and the time she took to type today ?
1. 20 min
2. 30 min
3. 10 min
4. 40 min
5. 1 hour
6. Yesterday Shweta completed 300 units of work at the rate of 15 units per minute. Today she com pleted the same units of work but her speed was 40% faster than yesterday. What is the approximate difference in the time she took today ?
1. 16 min
2. 26 min
3. 46 min
4. 36 min
5. 6 min
7. 12 men can complete one-third of the work in 8 days. In how many days can 16 men complete that work ?
1. 18
2. 12
3. 24
4. Cannot be determined
5. None of the above
8. 18 women can complete a work in 12 days and 12 men can complete the same work in 9 days. In how many days will 8 men and 8 women complete that work ?
1. 9
2. 6
3. 12
4.  8
5. None of these
9. 24 men can complete a piece of work in 15 days. In how many days will 18 men complete that work ?
1. 16 days
2. 20 days
3. 22 days
4. 25 days
5. None of these
10. 22 Men can complete a job in 16 days. In how many days will 32 Men complete that job ?
1. 14
2. 12
3. 16
4.  9
5. None of these
11. 10 Men can complete a piece of work in 8 days. In how many days can 16 men complete that work ?
1. 4 days
2. 5 days
3. 6 days
4. 3 days
5. None of these
12. 16 Men can complete a piece of work in 7 days. In how many days will 28 men complete the same work ?
1. 6 days
2. 8 days
3. 3 days
4. 4 days
5. None of these
13. A alone can make 100 baskets in 6 days and B alone can make 100 baskets in 12 days. In how many days can A and B together make 100 baskets ?
1. 3 days
2. 5 days
3. 2 1/2 days
4. 3 1/2 days
5. None of these
14. A single person takes 8 minutes to type a page. If from 1.00 pm to 2.00 pm, 1710 pages are to be typed, how many persons should be employed on this job ?
1. 207
2. 221
3. 249
4. 256
5. None of these
15. A single person takes 3 min to write a letter. If from 10 am to 12:00 noon, 1960 letters are to be written, how many persons should be employed on this job ?
1. 53
2. 47
3. 51
4. 49
5. None of these
Solutions :

1.

Given, A and B can complete a task in 4 days.

Therefore, work done by (A+B) in 1 day = 1/4

Work done by A alone in 1 day = 1/12
Therefore, work done by B alone in 1 day = (1/4) - (1/12) = (3-1) / 12 = 1/6

Hence, B alone can complete the work in 6 days.

2.

Given, A and B can complete a task in 8 days.

Therefore, work done by (A+B) in 1 day = 1/8

Work done by B alone in 1 day = 1/10

Therefore, work done by A alone in 1 day = (1/8) - (1/10) = (5-4) / 40 = 1/40

Hence, A alone can complete the work in 40 days.

3.

Given, A and B can complete a task in 6 days.

Therefore, work done by (A+B) in 1 day = 1/6

Work done by A alone in 1 day = 1/10

Therefore, work done by B alone in 1 day = (1/6) - (1/10) = (5-3) / 30 = 2/30 = 1/15

Hence, B alone can complete the work in 15 days

4.

Given, A and B can complete a task in 4 days.

Therefore, work done by (A+B) in 1 day = 1/4

Work done by A alone in 1 day = 1/6

Therefore, work done by A alone in 1 day = (1/4) - (1/6) = (3-2) / 12 = 1/12

Hence, B take 12 days to complete the work

5.

The time took to type yesterday = 5000/60 min = 83.33 min

Priti's speed of typing today = 60 words per min + 15% of 60 words per min

= 60 + 9 = 69 words per min

The time took to type today = 5000/69 min = 72.46 min

So, Required difference = 83.33 - 72.46

This is approximately equals to 10 min
6.

The time she taken to complete the work yesterday

= 300/15 = 20 min

The rate of work done by sweta today = rate of yesterday + 40% of rate of yesterday

= 15 + 6 = 21 units per min

The time she taken to complete the work today = 300/21 = 14.2 min

So, the required difference = 20 - 14.2

This is approximately equals to 6 mins

7.

Here m1 = 12,  m2 = 16

w1 = 1/3, w2 = 1

d1 = 8,  d2 = ?

m1d1w2 = m2d2w1

12 x 8 x 1 = 16 x d2 x 1/3

d2 = 18 days

8.

12 days work of 18 women = 9 days work of 12 men

18 x 12 women = 19 x 12 men

2 women = 1 man

8 men + 8 women = 8 men + 8/2 men = 8 men + 4 men = 12 men

So, 8 men + 8 women or 12 men can do the work in 9 days (according to the question)

9.
Let 18 men can complete the same work in x days, then

18 : 24 :: 15 : x

18 x x = 24 x 15

x = (24 x 15) / 18 = 20 days

10.

Let 32 men can complete the same work in x days, then

32 : 22 ::16 : x

32 x x = 22 x 16

x = (22 x 16) / 32 = 11 days

11.

Let 16 men can complete the same work in x days, then

16 : 10 :: 8 : x

16 x x = 10 x 8

x = (10x8) / 16 = 5 days

12.

Let 28 men can complete the same work in x days, then

28 : 16 :: 7 : x

28 x x = 16 x 7

x = (16x7) / 28 = 4 days

13.

If A can do a work in x days and B can do the same work in y days, the both of them together complete that work in xy / (x+y) days

= (6 x 12) / 18 = 4 days

14.

In 1 hour (60 min)

60/8 pages written by 1 man

so, 1 page written by 8/60

1710 pages written by

(8/60) x 1710 = 228 men

15.

In 2 hours (120 min)

120/3 = 40 letters written by 1 man

40 letters written by 1 man

1 letter written by 1/40

so, 1960 letters written by

(1/40) x 1960 = 49 men