Aptitude Questions : Chain Rule Set 3

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  1. 10 machines can wash 20 cars in 6 hours. In how many hours can 15 machines wash 40 cars?
    A) 8
    B) 7
    C) 15
    D) 12
    E) 6
    Answer & Explanation
    A) 8
    Explanation:

    Washing cars is a work, so
    M1*H1*W2 = M2*H2*W1
    10*6*40 = 15*H2*20
    Solve, H2 = 8 hrs
  2. To build a house, 5 men take 60 days working 8 hours each day. In how many days 2 such houses can be built by 8 men working 10 hours each day?
    A) 75
    B) 50
    C) 20
    D) 60
    E) None of these
    Answer & Explanation
    D) 60
    Explanation:

    Building 1 house is 1, 2 houses is 2, so
    M1*D1*H1*W2 = M2*D2*H2*W1
    5*60*8*(2) = 8*D2*10*(1)
    Solve, D2 = 60
  3. 2 men and 4 women can complete a job in 5 days. Also same job can be completed by 3 men and 8 women in 3 days. In how many days, twice the job can be completed by 3 men and 3 women?
    A) 4
    B) 8
    C) 10
    D) 8.5
    E) 13
    Answer & Explanation
    B) 8
    Explanation:

    2m + 4w = 5D, so 10m + 20w = 1D
    3m + 8w = 3D, so 9m + 24w = 1D
    So, 10m + 20w = 9m + 24w
    Solve, 1m = 4w
    From 1st equation(2m + 4w = 5D), 2*4w + 4w = 5D, or 12 women can do in 5 days, so 1 women in 12*5 = 60 days.
    Now 3m+3w = 3*4w + 3w = 15 w
    1 women in 60 days, so 15 women in 60/15 = 4 days
    But we are required to find twice work, so 15 women 1 work in 4 days so twice work in 8 days
  4. A job that can be completed by 2 men and 6 women in 10 days will be completed by 5 men and 15 women in how many days?
    A) 2
    B) 3
    C) 5
    D) 4
    E) Cannot be determined
    Answer & Explanation
    D) 4
    Explanation:

    2m + 6w = 10 D
    Or 2(1m + 3w) = 10D
    Or 1m + 3w = 20D
    So 5(1m + 3w) = 20/5
    Or 5m + 15w = 4D
  5. There is sufficient food for 40 men for a 15 days picnic. If after 6 days 4 men leave, how many more days can the remaining men intake food?
    A) 8
    B) 5
    C) 10
    D) 1
    E) 3
    Answer & Explanation
    D) 1
    Explanation:

    After 6 days, now food is left for 40 men for (15-6) = 9 days, now same food is eaten by (40-4) = 36 men, let it last for x days, so
    40*9 = 36*x
    Solve, x = 10
    The food which was to last for 9 days for 40 men, now will last for 10 days for 36 men, so extra 1 day.
  6. A job is completed by 5 men or 7 women in 40 days, then in how many days thrice the job as previous will be completed by 5 men and 3 women?
    A) 27
    B) 28
    C) 38
    D) 84
    E) 90
    Answer & Explanation
    D) 84
    Explanation:

    5 m or 7 w
    5m + 3w
    Cross multiply and put in denominator
    Days = 40*5*7/ [5*3 +7*5] = 28
    so for thrice work, days = 28*3
  7. 10 women completed 2/7th of work in 18 days working 6 hours each day. After this 5 women left and 2 men joined. In how many days working same number of hours, the remaining work will get completed if 1 man is equal to 2 women?
    A) 50
    B) 55
    C) 70
    D) 58
    E) 62
    Answer & Explanation
    A) 50
    Explanation:

    Remaining work = 1 – 2/7 = 5/7
    After 18 days, 5 women left and 2 men joined so 4 women joined (1m = 2w), now number of women is 5+4 = 9, so
    10*18*6*(5/7) = 9*D2*6*(2/7)
    Solve, D2 = 50
  8. 20 carpets are to weave by 40 women in 50 days working 8 hours per day. After 20 days, order of 6 more carpets came. To complete the total work on time, how many more hours per day they will have to work?
    A) 2
    B) 4
    C) 5
    D) 10
    E) 12
    Answer & Explanation
    B) 4
    Explanation:

    First find the number of carpets weave in first 20 days, after which order of more carpets came. So,
    In 50 days, 20 carpets, so in 20 days 20*20/50 = 8 carpets
    So in remaining 30 days, (20-8) = 12 carpets can be weave working 8 hrs each day
    Now number of carpets is (12+6) = 18, let no of hours is x, so
    H1*W2 = H2*W1
    8*18 = x*12
    Solve, x = 12 hrs
    So more hrs = 12-8 = 4 hrs
  9. A work is to completed. 10 men started the work and completed 1/6th of the work in 5 days working 3 hrs each day. 2 more men are employed. In how many days will the total number of men complete four times work as before working 5 hours each day?
    A) 12
    B) 18
    C) 10
    D) 20
    E) 15
    Answer & Explanation
    C) 10
    Explanation:

    M2 = (10+2) = 12 men, W2 = 4*(1/6) = 4/6
    So
    10*5*3*(4/6) = 12*D2*5*(1/6)
    Solve, D2 = 10
  10. 2 men or 4 women or 5 children can complete a piece of work in 38 days. In how many days will 1 man, 1 woman and 1 child complete the same work?
    A) 20
    B) 40
    C) 36
    D) 42
    E) None of these
    Answer & Explanation
    B) 40
    Explanation:

    2 men or 4 women or 5 children = 38 D
    So 1m + 1w + 1c = 38*2*4*5/(2*4 + 4*5 + 5*2)
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