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Aptitude Questions: Time And Work Set 8

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Hello Aspirants. Welcome to Online Quantitative Aptitude Section with explanation in AffairsCloud.com. Here we are creating question sample in Time and Work, which is common for all the competitive exams . We have included Some questions that are repeatedly asked in bank exams !!

  1. A and B alone can do a piece of wok in 8 and 18 days respectively. In how many days the work will be completed if they both work on alternate days starting with B?
    A) 6 5/9 days
    B) 5 days
    C) 10 7/9 days
    D) 10 9/7 days
    E) 6 2/9 days
    C) 10 7/9 days
    Explanation:

    A = 8 days, B = 18 days
    Total work = LCM(8,18) = 72
    So efficiency of A = 72/8 = 9, efficiency of B = 72/18 = 4
    2 days work of (A+B) = 9+4 = 13
    2*5(10) days work of (A+B) = 9+4 = 13*5 = 65
    So remaining work = 72-65 = 7
    Now A’s turn on 6th day, he will do remaining work(7) in 7/9 day
    So total 10 7/9 days

  2. A, B and C can all together do piece of work in 10 days, in which B takes three times as long as A and C together do the work and C takes twice as long as A and B together take to do the work. In how many days B can alone do the work?
    A) 35 days
    B) 33 days
    C) 43 days
    D) 40 days
    E) 45 days
    D) 40 days
    Explanation:

    (A+C) in x days so B completes in 3x days
    then (1/x) + (1/3x) = 1/10
    solve, x = 40/3
    so B in 3x = 3*(40/3)= 40 days
    OR
    Given A+B+C = 10 and that B takes 3 times as A+C, so A+C is three times stronger than B
    So this means that 4 times stronger can do work in 10 days
    So 1 time stronger(B) in 4*10 = 40 days

  3. 20 men can complete a piece of work in 14 days. 7 men started the work and after 20 days, 7 more men joined the work. In how many days the remaining work will be completed?
    A) 18 days
    B) 20 days
    C) 8 days
    D) 12 days
    E) 10 days
    E) 10 days
    Explanation:

    Let (7+7) complete remaining work in x days. So
    20*14 = 7*20 + 14*x
    x = 10 days

  4. 20 men can complete a work in 14 days and 20 women can complete the same work in 18 days. 7 men and 9 women started the work. After working for some days, they were replaced by 10 men and 10 women who complete the remaining work in 9 days. How much work was completed by initially employed men and women?
    A) 2/5
    B) 3/7
    C) 4/7
    D) 3/8
    E) None of these
    B) 3/7
    Explanation:

    20 m in 14 days so 10 men in (20*14)/10 = 28 days
    20 w in 18 days so 10 women in (20*18)/10 = 36 days
    So (1/28 + 1/36)*9 = 4/7
    So 1 – 4/7 = 3/7 work was done by 7 men and 9 women

  5. A, B and C can alone complete a work in 10, 12 and 15 days respectively. A and C started the work and after working for 4 days, A left and B joined. In how many days the total work was completed?
    A) 6 5/9 days
    B) 6 2/9 days
    C) 6 days
    D) 5 4/9 days
    E) 7 2/9 days
    B) 6 2/9 days
    Explanation:

    (A+C) = (1/10 + 1/15) = 1/6. They worked for 4 days so did (1/6)*4 = 2/3rd of work
    Remaining work = 1 – 2/3 = 1/3
    Now A left , B and C working
    (B+C) = (1/12 + 1/15) = 9/60 = 3/20. They worked for x days and completed 1/3rd of work so (3/20)*x = 1/3, so x = 20/9 days
    Total = 4 + 20/9

  6. A, B and C can alone complete a work in 10, 12 and 15 days respectively. All started the work but B left the work 3 days before completion. How much work was then done by A and B together in the total work?
    A) 2/3
    B) 3/4
    C) 1/3
    D) 3/5
    E) 2/5
    A) 2/3
    Explanation:

    Let work completed in x days, so A and C worked for all x days, and B for (x-3) days. So
    (1/10 + 1/15)*x + (1/12)*(x-3) = 1
    Solve, x = 5 days
    In 5 days, A did 5/10 = 1/2 of work
    In (5-3) = 2 days, B did 2/12 = 1/6 of work
    So total by A and B = (1/2 + 1/6) = 2/3

  7. 2 men and 3 women can together complete a piece of work in 4 days and 3 men and 2 women together can complete work in 3 days. In how many days 10 women will complete this work?
    A) 9 days
    B) 6 days
    C) 7 days
    D) 12 days
    E) 10 days
    B) 6 days
    Explanation:

    2m + 3w = 4, 3m + 2w = 3
    So 4(2m + 3w) = 3(3m + 2w)
    8m + 12w = 9m + 6w
    6w = 1m
    Given 2m + 3w = 4, so 2*(6w) + 3w = 4, so 15 women in 4 days, so 10 women in (15*4)/10 = 6 days

  8. A alone can complete a work in 5 days more than A+B together and B alone can complete a work in 45 days more than A+B together. Then in how many days A and B together can complete the work?
    A) 16 days
    B) 21 days
    C) 15 days
    D) 20 days
    E) 25 days
    C) 15 days
    Explanation:

    Shortcut = √5×45 = 15
    OR
    Let (A+B) can do in x days, so
    1/(x+5) + 1/(x+45) = 1/x
    Solve, x2 = 225, x = 15

  9. 20 men can complete a work in 14 days and 20 women can complete the same work in 18 days. 8 men start the work and after working for 21 days, they are replaced by x women. If the remaining work is to be completed by x women in 9 days, then how many women should be employed?
    A) 18
    B) 24
    C) 20
    D) 16
    E) 15
    D) 16
    Explanation:

    20 m in 14 days so 8 men in (20*14)/8 = 35 days
    In 21 days 8 men complete (1/35)*21 = 3/5 work
    Remaining work = 1 – 3/5 = 2/5
    20 women do 1 work in 18 days so x women will do 2/5 work in 9 days
    10*(2/5)*18 = x*1*9

  10. A alone can complete a work in 21 days. If B is 40% more efficient than A, then in how many days A and B together can complete the work?
    A) 8 1/4 days
    B) 8 3/4 days
    C) 9 days
    D) 10 3/4 days
    E) 11 1/3 days
    B) 8 3/4 days
    Explanation:

    Let efficiency of A is x, so of B = (140/100)*x = 7x/5
    So ratio of efficiencies = x : 7x/5 = 5 : 7
    So ratio of days = 7 : 5
    A can do in 21 days, so 7y = 21, y = 3
    So B can do in 5*3 = 15 days
    A+B in (21*15)/(21+15) = 8 ¾ days