Time & Work, General Mathematics

Question: A can do a piece of  work in 30 days while B alone can do it in 40 days.
In how many days can A and B working together do it ?
A17`1/7`

B27`1/7`

C42`3/4`

D70

Note: solution:
A's 1 day's work= `1/30` & B's 1 day's work = `1/40`.
`:.`(A+B)' s 1 day's work =`(1/30 + 1/40) = 7/120`.
`:.`Both together will finish the work in `120/7 =17 1/7` days.

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Question: A and B together can complete a piece of work in 35 days while A alone can complete the same work in 60 days. B alone will be able to complete the same work in :
A42 days

B72 days

C84 days

D96 days

Note: solution:
(A + B)'s  1 day's work = `1/35` 
     & A's 1 day's work = `1/60`.
`:.` B's 1 day's work = `(1/35 - 1/60)`
                      = `5/420`
                      = `1/184`.
Hence B alone will finish the work in 84 days.

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Question: 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 to do it, working together 8 2/5 hours a day ?
A3 days

B4 days

C4 1/2 days

DNone of these

Note: solution:
A  can complete the work in `(7 xx 9)` hrs = 63 hrs.
B can complete the work in  `(6 xx 7)` hrs = 42 hrs.
 `:.` A's 1 hour's work = `1/63` 
    &  B's 1 hour's work = `1/42`.
`(A + B)`'s 1 hour's work = `(1/63 + 1/42)`
                         = `5/126`.
`:.` Both will finish the work in `(126/5)` hrs.
Number of days of `8 2/5` hrs each =  `(126/5 xx 5/42)`
                                  =  3 days.

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Question: A can do a piece of work in 15 days and B alone can do it in 10 days. B work at it for 5 days and then leaves. A alone can finish the remaining work in :
A`6 1/2` days

B`7 1/2` days

C8 days

D9 days

Note: solution:
B's 5 day's work = `(1/10 xx 5)`
                           = `1/2`.
Remaining work = `(1 - 1/2)`
                          = `1/2`.
A can do `1/2` work in `7 1/2` days.

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Question: A can do `1/3` of the work in 5 days and B can do `2/5` of the work in 10 days. In how many days both A and B together can do the work ?
A`7 3/4`

B`8 4/5`

C`9 3/8`

D10

Note: solution:
Whole work will be done by A in `(5 xx 3)`
                                   = `15` days.
Whole work will be done by B in `(10 xx 5/2)`
                                   = `25` days.
A's 1 day's work = `1/15` &
 B's 1 day's work = `1/25`.
`(A + B)`'s 1 day's work = `(1/15 + 1/25)`
                                       = `8/75`.
So, both together can finish it in `75/8`
                                    =`9 3/8` days.

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Question: A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. The two together could complete the work in :
A24 days

B25 days

C30 days

D35 days

Note: solution:
Work done by A in 10 days = `(1/80 xx 10)` 
                                           = `1/8`.
Remaining work =`(1 - 1/8)`
                          = `7/8`.
Now, `7/8` work is done by B in 42 days
Whole work will be done by B in `(42 xx 8/7)`
                                                    = 48 days.
`:.` A's 1 day's work = `1/80` &
      B's 1 day's work = `1/48`.
`:. (A + B)`'s 1 day's work =`(1/80 + 1/48)`
                                        =`8/240`
                                        =`1/30`.
Hence, both will finish the work in 30 days.

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Question: A and B can together finish a work in 30 days. They worked at it for 20 days and then B left. the remaining work was done by A alone in 20 more days. A alone can finish the work in :
A48 days

B50 days

C54 days

D60 days

Note: solution:
Work done by A and B in 20 days = `(1/30 xx 20)`
                                                      =`2/3`.
Remaining work =`(1 - 2/3)`
                           =`1/3`.
Now, `1/3` work is done by A in 2o days
`:.` Whole work will be done by A in `(20 xx 3) = 60` days.

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Question: A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but a leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was :
A6

B8

C9

D12

Note: solution:
`(A + B)`'s 1 day's work = `(1/45 + 1/40)`
                                   =`17/360`.
Work done by B in 23 days = `(1/40 xx 23)`
                                       =`23/40`.
Remaining work = `(1 - 23/40)`
                       =`17/40`.
Now, `17/360` work was done by `(A + B)` in `(1 xx 360/17 xx 17/40)`
                                                                  = 9 days.
`:.`A left after 9 days.

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Question: A dose half as much work as B in three-fourth of the time. If  together they take 18 days to complete the work, how much time shall B take to do it ?
A30 days

B35 days

C40 days

Dnone of these

Note: solution:
Suppose B takes `X` days to do the work.
`:.` A takes `(2 xx 3/4 x)` 
                    = `(3x)/2` days to do it.
`(A + B)`'s 1 day's work = `1/18`.
`:. 1/x + 2/(3x) = 1/18` 
  or `x = 30`.

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Question: A can do a certain job in 12 days. B is 60% more efficient than A. The number of days, it take  B to do the same piece of  work, is :
A6

B`6 1/4`

C`7 1/2`

D8

Note: solution:
Ration of times taken by A and B =`160 : 100 = 8 : 5`.
`8 : 5 :: 12 : X`
or `8x = 5 xx 12`
or `x = 7 1/2` days.

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Question: A can do a piece of work in 30 days while B alone can do it in 40 days. In how many days can A and B working together do it ?

Question: A and B together can complete a piece of work in 35 days while A alone can complete the same work in 60 days. B alone will be able to complete the same work in :

Question: 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 to do it, working together 8 2/5 hours a day ?

Question: A can do a piece of work in 15 days and B alone can do it in 10 days. B work at it for 5 days and then leaves. A alone can finish the remaining work in :

Question: A can do `1/3` of the work in 5 days and B can do `2/5` of the work in 10 days. In how many days both A and B together can do the work ?

Question: A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. The two together could complete the work in :

Question: A and B can together finish a work in 30 days. They worked at it for 20 days and then B left. the remaining work was done by A alone in 20 more days. A alone can finish the work in :

Question: A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but a leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was :

Question: A dose half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it ?

Question: A can do a certain job in 12 days. B is 60% more efficient than A. The number of days, it take B to do the same piece of work, is :