TIME AND WORK PRACTICE WORD PROBLEMS

1. Rafiq can do a work in 10 days and Shafiq can do that in 15 days. In how many days do they together finish the work ?

2. A can do a work in p days and B can do it in 2p days. They started to do the work together and after some days A left the work unfinished. B completed the rest of the work in r days. In how many days was the work finished ?

3. 10 persons can do a work in 7 days by working 6 hours. Working how many hours per day can 14 persons finish the work in 6 days ?

4. Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A and B, working together but independently to do the sane job ?

5. A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete the work ?

6.  A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 hours each. How long will they take it do it, working together 8  2/5 hours a day ?

7. A and B can do a piece of work in 18 days, B and C can do it in 24 days. A and C can do it in 36 days. In how many days will A, B and C finish it, working together and separately ?

1. Answer :

Let "d" be the number days taken by together to finish the work.

Rafiq is taking 10 days to complete the work and Shafiq is taking 15 days.

Work done by Rafiq in 1 day  =  1/10

Work done by Shafiq in 1 day  =  1/15

Part of work done by Rafiq in d days  =  d/10

Part of work done by Shafiq in d days  =  d/15

Part of work finished by both in d day  =  d/10 + d/15

In d days they are finishing the work :

d/10 + d/15  =  1

5d/30  =  1

5d  =  30

d  =  6

So, they will take 6 days to complete the work.

2. Answer :

Time taken by A   =  p days

A's one day work  =  1/p

Time taken by B   =  2p days

B's one day work  =  1/2p

Let x be the number of days they work together.

Work done in x days  =  x(1/p + 1/2p)

=  x(3/2p)

Unfinished work  =  1 - (3x/2p)

To finish the remaining work, B is taking r days.

work finished in r days  =  r (1/1-(3x/2p))

=  r(2p/2p-3x)

r(2p/2p-3x)  =  2p

r  =  2p-3x

3x  =  2p-r

x  =  (2p-r)/3

Number of days taken to complete the work  =  x + r

= (2p-r)/3 + r

=  (2p+2r)/3

=  (2/3)(p+r)

3. Answer :

By comparing persons and hours,

if number of persons increased then hours taken will reduce. So, it comes under inverse proportion.

By comparing days and hours,

if the days increased then hours taken will reduce. So, it also comes under inverse proportion.

10 ⋅ 6  =  14 ⋅ x     and        7 ⋅ 6  =  6 ⋅ x

So, 

10 ⋅ 6 ⋅ 7  =  14 ⋅ x ⋅ 6

x  =  (10 ⋅ 6 ⋅ 7) / (14 ⋅ 6)

x  =  (10 ⋅ 6 ⋅ 7) / (14 ⋅ 6)

x  =  5 h

Therefore, the required number of hours is 5 hours.

4. Answer :

Work done by A in one hour = 1/8

Work done by B in one hour = 1/10

Amount of work done by A and B = (1/8 + 1/10)

= (5 + 4)/40

= 9/40

Both A and B will finish the work in 40/9

= 4  4/9 days

5. Answer :

Portion of work completed by A and B in one day = 1/4

Portion of work completed by A in one day = 1/12

Portion of work completed by B in one day = 1/4 - 1/12

= (3 - 1)/12

= 2/12

= 1/6

Number of day = 1/(1/6)

= 6 days

Number of days completed by B is 6 days.

6. Answer :

Number of hours taken by A = 7 x 9

= 63 hours

Number of hours taken by B = 6 x 7

= 42 hours

Work done by A in one hour = 1/63

Work done by B in one hour = 1/42

work done by A and B in one hour = 1/63 + 1/42

= 5/126

Time in hours = 1/(5/126)

= 126/5

Number of days of 8  2/5 hours each = (126/5) / 8  2/5

= (126/5) / (42/5)

= (126/5) x (5/42)

= 3 days

7. Answer :

Work done by A and B in one day = 1/18

Work done by B and C in one day = 1/24

Work done by C and A in one day = 1/36

Work done by A, B and C in one day

2(A + B + C) = 1/18 + 1/24 + 1/36

= (4 + 3 + 2)/72

= 9/72

2(A + B + C ) = 1/8

(A + B + C ) = 1/16

Number of days = 1/(1/16)

= 16 days

A's one day work = 1/16 - 1/24

= (3 - 2)/48

= 1/48

number of days taken by A = 48

B's one day work = 1/16 - 1/36

= (9-4)/144

= 5/144

Number of days taken by B = 144/5

= 28.8 days

C' one day work = 1/16 - 1/18

= (9 - 8)/144

= 1/144

Number of days taken by C = 1/(1/144)

= 144 days

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