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### 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 **:

**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 ?****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 ?**- 28
- 36
- 40
- 32
- None of these
**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 ?**- 15
- 16
- 14
- 12
- None of these
**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 ?**- 8
- 17
- 14
- 12
- None of these
**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 ?**- 20 min
- 30 min
- 10 min
- 40 min
- 1 hour
**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 ?**- 16 min
- 26 min
- 46 min
- 36 min
- 6 min
**12 men can complete one-third of the work in 8 days. In how many days can 16 men complete that work ?**- 18
- 12
- 24
- Cannot be determined
- None of the above
**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 ?**- 9
- 6
- 12
- 8
- None of these
**24 men can complete a piece of work in 15 days. In how many days will 18 men complete that work ?**- 16 days
- 20 days
- 22 days
- 25 days
- None of these
**22 Men can complete a job in 16 days. In how many days will 32 Men complete that job ?**- 14
- 12
- 16
- 9
- None of these
**10 Men can complete a piece of work in 8 days. In how many days can 16 men complete that work ?**- 4 days
- 5 days
- 6 days
- 3 days
- None of these
**16 Men can complete a piece of work in 7 days. In how many days will 28 men complete the same work ?**- 6 days
- 8 days
- 3 days
- 4 days
- None of these
**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 ?**- 3 days
- 5 days
- 2 1/2 days
- 3 1/2 days
- None of these
**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 ?**- 207
- 221
- 249
- 256
- None of these
**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 ?**- 53
- 47
- 51
- 49
- 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

= 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

= 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

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)

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

18 : 24 :: 15 :

18 x

Let 32 men can complete the same work in

32 : 22 ::16 :

32 x

Let 16 men can complete the same work in

16 : 10 :: 8 :

16 x

Let 28 men can complete the same work in

28 : 16 :: 7 :

28 x

If A can do a work in

= (6 x 12) / 18 = 4 days

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

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

*x*days, then18 : 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, then32 : 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, then16 : 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, then28 : 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*x**y*/ (*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

**Shared by**

*Shravan Varma Gadhiraju*
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