Quantitative Aptitude: Time and Work Set 17

  1. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
    70
    50
    80
    60
    100
    Option D
    Let A’s 1 day’s work = x and B’s 1 day’s work = y
    Then, x + y = 1/30 and 16x + 44y = 1
    Solving these two equations, we get: x =1/60 and y =1/60
    B’s 1 day’s work = 1/60
    B alone shall finish the whole work in 60 days

     

  2. P takes twice as much time as Q or thrice as much time as R to finish a piece of work. They can finish the work in 2 days if work together. How much time will Q take to do the work alone?
    4
    5
    6
    7
    8
    Option C
    Let P takes x days to complete the work
    Then Q takes x/2 days and R takes x/3 days to finish the work
    Amount of work P does in 1 day = 1/x
    Amount of work Q does in 1 day = 2/x
    Amount of work R does in 1 day = 3/x
    Amount of work P,Q and R do in 1 day = 1/x + 2/x + 3/x = 1/x (1 + 2 + 3) = 6/x
    6/x = 2
    => x = 12
    => Q takes 12/2 days = 6 days to complete the work

     

  3. 10 men can complete a work in 7 days. But 10 women need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work?
    7
    10
    9
    8
    6
    Option A
    Work done by 10 men in 1 day = 1/7
    Work done by 1 man in 1 day = (1/7)/10 = 1/70
    Work done by 10 women in 1 day = 1/14
    Work done by 1 woman in 1 day = 1/140
    Work done by 5 men and 10 women in 1 day = 5 × (1/70) + 10 × (1/140)
    = 5/70 + 10/140 = 1/7
    => 5 men and 10 women can complete the work in 7 days

     

  4. 3 men and 7 women can complete a work in 10 days . But 4 men and 6 women need 8 days to complete the same work . In how many days will 10 women complete the same work?
    50
    30
    60
    40
    20
    Option D
    Work done by 4 men and 6 women in 1 day = 1/8
    Work done by 3 men and 7 women in 1 day = 1/10
    Let 1 man does m work in 1 day and 1 woman does w work in 1 day.
    4m + 6w = 1/8 —(1)
    3m + 7w = 1/10 —(2)
    Solving equation (1) and (2) , we get m=11/400 and w=1/400
    Amount of work 10 women can do in a day = 10 × (1/400) = 1/40
    40 days

     

  5. P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. how many days does P alone need to finish the remaining work?
    9
    6
    8
    5
    7
    Option B
    Work done by P in 1 day = 1/18
    Work done by Q in 1 day = 1/15
    Work done by Q in 10 days = 10/15 = 2/3
    Remaining work = 1 – 2/3 = 1/3
    Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6

     

  6. A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
    34 ½
    38 ½
    30 ½
    37 ½
    31 ½
    Option D
    Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 — (1)
    Work done by A and B in 3 days = 20/100 = 1/5
    Work done by A and B in 1 day = 1/15 —(2)
    Work done by B in 1 day = 1/15 – 1/25 = 2/75
    => B can complete the work in 75/2 days = 37 ½ days

     

  7. A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. How much time will B alone take to complete the work (in hours).
    10
    17
    12
    14
    16
    Option C
    Work done by A,B and C in 1 hour = 1/4+1/3 = 7/12
    Work done by B in 1 hour = 7/12 – 1/2 = 1/12
    B = 12 hours

     

  8. A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?
    300
    100
    200
    400
    500
    Option D
    Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24
    Amount of work A + B + C can do = 1/3
    Amount of work C can do in 1 day = 1/3 – 7/24 = 1/24
    work A can do in 1 day: work B can do in 1 day: work C can do in 1 day
    = 1/6 : 1/8 : 1/24 = 4 : 3 : 1
    Amount to be paid to C = 3200 × (1/8) = 400

     

  9. P and Q were assigned to do a work for an amount of 1200. P alone can do it in 15 days while Q can do it in 12 days. With the help of R they finish the work in 6 days. Find the share if C.
    100
    130
    140
    120
    150
    Option D
    Total work = 1/15 + 1/12 + 1/c = 1/6
    To complete the whole work by C = 60
    so ratio of work done by P:Q:R = 4:5:1
    so c share = (1/10)*1200 = 120

     

  10. A does half as much work as B does in one sixth of the time. If together they take 20 days to complete the work, then what is the time taken by B to complete the work independently.
    70
    60
    50
    80
    90
    Option D
    Let B take X days to complete the work then in one –sixth of the time i.e. x/6 days.
    Now A do half work as done by B so A will take twice the time.
    2*x/6 = x/3 to complete the job alone
    1/x + 3/x = 1/20
    x = 80 days

     


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