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Time and Work Questions Answers

  • 15. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C

    1. Rs. 300
    2. Rs. 400
    3. Rs. 500
    4. Rs. 600
    Answer And Explanation

    Answer: Option B

    Explanation:

    C's 1 day's work =
    \begin{aligned}
    \frac{1}{3}- \left(\frac{1}{6} +\frac{1}{8} \right) \\
    =\left(\frac{1}{3} - \frac{7}{24} \right) \\
    = \frac{1}{24} \\
    A:B:C = \frac{1}{6}:\frac{1}{8}:\frac{1}{24} \\
    = 4:3:1 \\
    C's Share = \frac{1}{8}* 3200 \\
    = 400
    \end{aligned}
    If you are confused how we multiplied 1/8, then please study ratio and proportion chapter, for small information, it is the C ratio divided by total ratio.

  • 16. 4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women working together finish it ?

    1. 30 days
    2. 40 days
    3. 50 days
    4. 60 days
    Answer And Explanation

    Answer: Option B

    Explanation:

    Let 1 man's 1 day work = x
    and 1 woman's 1 days work = y.
    Then, 4x + 6y = 1/8
    and 3x+7y = 1/10
    solving, we get y = 1/400 [means work done by a woman in 1 day]

    10 women 1 day work = 10/400 = 1/40

    10 women will finish the work in 40 days

  • 17. A piece of work can be done by 6 men and 5 women in 6 days or 3 men and 4 women in 10 days. It can be done by 9 men and 15 women in how many days ?

    1. 3 days
    2. 4 days
    3. 5 days
    4. 6 days
    Answer And Explanation

    Answer: Option A

    Explanation:

    To calculate the answer we need to get 1 man per day work and 1 woman per day work.

    Let 1 man 1 day work =x
    and 1 woman 1 days work = y.
    => 6x+5y = 1/6
    and 3x+4y = 1/10
    On solving, we get x = 1/54 and y = 1/90

    (9 men + 15 women)'s 1 days work =
    (9/54) + (15/90) = 1/3

    9 men and 15 women will finish the work in 3 days


  • 18. 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 wotk were ?

    1. \begin{aligned} 14\frac{2}{3}kmph \end{aligned}
    2. \begin{aligned} 15\frac{2}{3}kmph \end{aligned}
    3. \begin{aligned} 16\frac{2}{3}kmph \end{aligned}
    4. \begin{aligned} 17\frac{2}{3}kmph \end{aligned}
    Answer And Explanation

    Answer: Option C

    Explanation:

    Work done by A in l0 days = (1/25) *10 = 2/5
    Remaining work = 1 - (2/5) = 3/5
    (A+B)s 1 days work = (1/25) + (1/20) = 9/100

    9/100 work is done by them in 1 day.
    hence 3/5 work will be done by them in (3/5)*(100/9)
    = 20/3days.

    Total time taken = (10 + 20/3) = 16*(2/3) days

  • 19. 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

    1. 6 days
    2. 7 days
    3. 8 days
    4. 9 days
    Answer And Explanation

    Answer: Option B

    Explanation:

    1 woman's 1 day's work = 1/70
    1 Child's 1 day's work = 1/140
    5 Women and 10 children 1 day work =
    \begin{aligned}
    \left(\frac{5}{70}+\frac{10}{140}\right) \\
    = \frac{1}{7}
    \end{aligned}

    So 5 women and 10 children will finish the work in 7 days.

  • 20. A alone can complete a work in 16 days and B alone can do in 12 days. Starting with A, they work on alternate days. The total work will be completed in

    1. \begin{aligned} 13\frac{1}{4} \end{aligned}
    2. \begin{aligned} 13\frac{1}{2} \end{aligned}
    3. \begin{aligned} 13\frac{3}{4} \end{aligned}
    4. \begin{aligned} 13\frac{4}{4} \end{aligned}
    Answer And Explanation

    Answer: Option C

    Explanation:

    A's 1 day work = 1/16
    B's 1 day work = 1/12

    As they are working on alternate day's
    So their 2 days work = (1/16)+(1/12)
    = 7/48

    [here is a small technique, Total work done will be 1, right, then multiply numerator till denominator, as 7*6 = 42, 7*7 = 49, as 7*7 is more than 48, so we will consider 7*6, means 6 pairs ]

    Work done in 6 pairs = 6*(7/48) = 7/8

    Remaining work = 1-7/8 = 1/8

    On 13th day it will A turn,
    then remaining work = (1/8)-(1/16) = 1/16

    On 14th day it is B turn,

    1/12 work done by B in 1 day

    1/16 work will be done in (12*1/16) = 3/4 day

    So total days =
    \begin{aligned} 13\frac{3}{4} \end{aligned}

    It may be a bit typical question, but if are not getting it in first try then give it a second try. Even not, then comment for explanation for this. We will be happy to help you.

  • 21. 5 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio

    1. 1:2
    2. 1:3
    3. 2:1
    4. 2:3
    Answer And Explanation

    Answer: Option C

    Explanation:

    Let 1 man 1 day work = x
    1 boy 1 day work = y

    then 5x + 2y = 4(x+y)
    => x = 2y
    => x/y = 2/1
    => x:y = 2:1