Time & Work
 

  1. Question: A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 days. The number of days taken in completing the work was:

    A
    `12 1/2`

    B
    `14 2/9`

    C
    15

    D
    `16 2/3`

    Note: solution: Work done by A in 10 days = `(1/25 xx 10)` = `2/5`. Remaining work = `(1 - 2/5)` = `3/5`. `(A +B)`'s 1 day's work = `(1/25 + 1/20)` = `9/100`. Now, `9/100` work is done by them in 1 day. `:. 3/5` work will be done by them in `(100/9 xx 3/5) = 20/3` days. Total time taken = `(10 + 20/3)` = `16 2/3` days.
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  2. Question: A is twice as good a workman as B and together they finish a piece of work in 14 days. The number of days taken by A alone to finish the work, is :

    A
    11

    B
    21

    C
    28

    D
    42

    Note: solution: (A's 1 day's work) : (B's 1 day's work ) =`2 : 1` `(A + B)`'s 1 day's work = `1/14`. Divide `1/14` in the ratio `2 : 1`. `:.` A's 1 day's work = `(1/14 xx 2/3 )` = `1/21`. Hence, A alone can finish the work in 21 days.
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  3. Question: A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. B alone can do the whole work in:

    A
    12 days

    B
    15 days

    C
    20 days

    D
    30 days

    Note: solution: Ratio of times taken by `A & B = 1 : 3`. If difference of time is 2 days, B takes 3 days. If difference of time is 10 days, B takes `(3/2 xx 10)` = `15` days.
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  4. Question: A can do a piece of work in 14 days which B can do in 21 days. They begin together but 3 days before the completion of the work, A leaves off. The total number of days to complete the work is :

    A
    `6 3/5`

    B
    `8 1/2`

    C
    `10 1/5`

    D
    `13 1/2`

    Note: solution: B's 3 day's work =`(1/21 xx 3)` = `1/7`. Remaining work =`(1 - 1/7)` = `6/7` `(A + B)`'s 1 day's work = `(1/14 + 1/21)` =`5/42`. Now, `5/42` work is done by A & B in 1 day. `:. 6/7` work in done by A & B in `(42/5 xx 6/7)` =`36/5` days. `:.` Total time taken = `(3 + 36/5)` days = `10 1/5` days.
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  5. Question: If Ramesh, Suresh and Harish can do a piece of work in 15 days, 10 days and 6 days respectively, how long will they take to do it, if all the three work at it together ?

    A
    3 days

    B
    `3 1/2` days

    C
    `3 9/20` days

    D
    `3 3/20` days

    Note: solution: (Ramesh + Suresh + Harish)'s 1 day's work = `(1/15 + 1/10 + 1/6)` =`12/30` =`1/3`. So, all the tree will finish the work in 3 days.
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  6. Question: A and B can do a piece of work in 72 days; B and C do it in 120 days; A and C can do it in 90 days. In what time can A alone do it ?

    A
    150 days

    B
    120 days

    C
    100 days

    D
    80 days

    Note: solution: `(A + B )`'s 1 day's work =`1/721`, `(B + C)`'s 1day's work =` 1/120`, `(A + C)`'s 1day's work =`1/90`. Adding `2(A + B + C)`'s 1 day's work = `(1/72 + 1/120 + 1/90)` =`12/360` =`1/30`. `:. (A + B + C)`'s 1 day's work =`1/60`. A's 1 day's work =`(1/60 - 1/120)` =`1/120`. `:.` A alone can finish the work in 120 days.
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  7. Question: A and B can do a piece of work in 5 days; B and C can do it in 7 days; A and C can do it in 4 days. Who among these will take the least time if put to do it alone ?

    A
    A

    B
    B

    C
    C

    D
    Data inadequate

    Note: solution: `(A + B)`'s 1 day's work = `1/5`; `(B + C)`'s 1 day's work = `1/7` and `(A + C)`'s 1 day's work = `1/4`. `2(A + B + C)`'s 1 day's work =`(1/5 + 1/7 + 1/4)` =`83/140`. `(A + B + C)`'s 1 day's work = `83/280`. C's 1 day's work =`(83/280 - 1/5)` = `27/280`. A's 1 day's work =`(83/280 - 1/7)` =`43/280`. B's 1 day's work =`(83/280 - 1/4)` =`13/280.` Thus time taken by A, B, C is `280/43` days, `280/13` days, `280/27` days respectively. Clearly, the time taken by A is least.
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  8. Question: If A, B and C together can finish a piece of work in 4 days; A alone can do it in 12 days and B in 18 days, then C alone Can do it in:

    A
    21 days

    B
    16 days

    C
    14 days

    D
    9 days

    Note: solution: `(A + B + C)`'s 1 day's work =`1/4` `(A + B)`'s 1 day's work =`(1/12 + 1/18)` =`5/36`. C's 1 day's work =`(1/4 - 5/36)` =`4/36` =`1/9`. `:.`C alone can finish the work in 9 days.
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  9. Question: 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 can they do it all working together ?

    A
    12

    B
    13

    C
    16

    D
    26

    Note: solution: `(A + B)`'s 1 day's work =`1/18`, `(B + C)`'s 1 day's work =`1/24` and `(A + C)`'s 1 day,s work =`1/36`. `:. 2 (A + B + C)`'s 1 day's work =`(1/18 + 1/24 + 1/36)` =`9/72` =`1/8` `:. (A + B + c)`'s 1 day's work =`1/16`. Hence, all working together can do the work in 16 days.
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  10. Question: A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes in 13 days. In how many days C alone will do the work?

    A
    16

    B
    24

    C
    36

    D
    48

    Note: solution: `(A + B)'s 5`days' work `+(B +C)`s 2 day's work `+ C's 11`day's work = 1. `5/12 + 2/16 + C's 11` day's work = 1 `C's 11` day's work = `11/24` `C's 1` day's work `= (11/24 xx 1/11)` `= 1/24`. `:.`C alone can finish it in 24 days.
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