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)