Quantitative Aptitude: Time and Work Set 20

1. 15 boys or 30 girls or 45 men can complete the work in 12 days. Find the number of days taken by 8 boys and 10 girls and 15 men to complete the work?
   
   
   12
   13
   10
   9
   8
   Option C
   15 boys= 30 girls
   
   1 boy = 2 girl
   
   15 boys = 45 men
   
   1 boy = 3 men
   
   8 boy + 10 girls + 15 men = 8 b + 5 b + 5 b = 18 boys
   
   boys ....... days
   
   15 ............... 12
   
   18 .............. ?
   
   (15 * 12) = (18 * x)
   
   x = (15 * 12) / 18 = 10 days
   
   
   
    



2. Kiran and Kishore do a certain work in 42 days and 30 days respectively.Kishore started the work alone and then after 6 days Kiran joined him till the completion of the work. How long did the work last?
   
   
   10
   20
   30
   40
   50
   Option B
   Work done by Kishore in 6 days = (1/30) * 6 = 1/5
   
   Remaining work = 1 – 1/5 = 4/5
   
   (Kiran + Kishore)’s 1 day work = 1/42 + 1/30
   
   = > (42 + 30) / (42 * 30)
   
   = > 2/35
   
   Together can complete the work in 35/2 days
   
   So 4/5 work will be done by both
   
   = > (4/5) * (35/2)
   
   = > 14 days
   
   Total time taken = 14 + 6 = 20 days
   
   
   
    



3. P alone can do a piece of work in x days. Q alone can do the same work in 10 days more than P. R alone can do the same work in 10 days. If all of them working together and completed the work in 5 5/11 days, then find the value of ‘x’?
   
   
   20
   30
   40
   50
   60
   Option A
   Given,
   
   (1/x) + (1/(x + 10)) + 1/10 = 11/60
   
   (1/x) + (1/(x + 10)) = 11/60 – 1/10
   
   (2x + 10) / (x2 + 10x) = 1/12
   
   24x + 120 = x2 + 10x
   
   x2 – 14x – 120 = 0
   
   x = 20, -6 (Eliminate –ve value)
   
   x = 20 days
   
   
   
    



4. A mother is 2 times faster than his daughter. If the daughter can complete a piece of work in 16 days, then how long will it take for both mother and daughter to complete the same piece of work?
   
   
   4 1/2
   3 1/3
   5 1/3
   2 1/5
   1 1/7
   Option C
   Efficiency ratio of mother and daughter = 2 : 1
   
   The day ratio of mother and daughter = 1 : 2 (x, 2x)
   
   2x = 16
   
   x = 8
   
   mother and dauhter’s one day work,
   
   = > (1/8) + (1/16)
   
   = > 3/16
   
   mother and daughter can complete a piece of work in,
   
   = > 16/3 = 5 1/3 days
   
   
   
    



5. 46 female labours earned Rs. 172500 by working 25 days. How many male labours must work for 24 days to receive Rs. 230400 provided the daily wages of a man is twice that of a female labour?
   
   
   20
   22
   30
   32
   40
   Option D
   1 F’s 1 day wages = Total wages / (Number of days * total F)
   
   = > 172500 / (46 * 25) = 150
   
   1 M’s 1 day wages = 2 * 1 F’s 1 day wages = 2 * 150 = 300
   
   Total F = 230400 / (24 * 300) = 32 M
   
   
   
    



6. 12 Male workers can complete a work in 15 days and 15 Female workers can complete the same work in 24 days. Then find 15 males and 20 Females can complete the work?
   
   
   7 1/5
   5 1/5
   3 1/5
   4 1/5
   10 1/5
   Option A
   Total work = M * days
   
   12 m * 15 = 15 f * 24
   
   1 m = 2 f
   15 m + 20 f = 15 m + 10 m = 25 m
   
   Males days
   
   12 15
   
   25 ?
   
   (12 * 15) = (25 * x)
   
   x = (12 * 15) / 25 = 36 / 5 = 7 1/5 days
   
    



7. Lal is 20 % more efficient than Taj to complete the work. Both of them together complete the work in 5 5/11 days. Find the number of days taken by Lal alone to complete the work?
   
   
   
   10
   11
   12
   13
   14
   Option A
   Efficiency ratio = > 120: 100 = 6: 5
   
   Day ratio = > 5: 6 (5x, 6x)
   
   According to the question,
   
   (1/5x) + (1/6x) = (11/60)
   
   (6x + 5x) / (30x2) = (11/60)
   
   11x / 30x2 = (11/60)
   
   x = 2
   
   The number of days taken by Lal alone to complete the work = 10 days
   
   
   
    



8. A garments wanted 40 women to complete a project in 15 days. 40 women started working, after 9 days they notices that only three-fifth of the work gets completed. Then how many extra women can be employed to complete the remaining work on time?
   
   
   0
   1
   2
   3
   4
   Option A
   women Days Work
   
   40 15 1
   
   40 9 3/5
   
   ? 6 2/5
   
   (40 * 9) / (3/5) = [(40 + x) * 6] / (2/5)
   
   40 = 40 + x
   
   x = 0
   
   There is no extra women needed to complete the work.
   
    



9. A and B can complete the work alone in x days and (x + 10) days respectively. They work together to complete the work in 6 2/3 days. Find the efficiency ratio of A to that of B?
   
   
   2 : 5
   2 : 1
   3 : 1
   2 : 7
   4 : 1
   Option B
   A = x days, B = (x + 10) days
   
   Given,
   
   (1/x) + (1/(x + 10)) = 1/(6 2/3)
   
   [x + x + 10] / [x (x + 10)] = 3/20
   (2x + 10) / (x2 + 10x) = 3/20
   
   40x + 200 = 3x2 + 30x
   
   3x2 – 10x – 200 = 0
   
   x = 10, -6.66 (negative value will be eliminated)
   
   So, x = 10
   
   The efficiency ratio of A and B = 1/10 : 1/20 = 2 : 1
   
   
   
    



10. 35 workers can complete a piece of work in 18 days. After 8 days from the start of the work, some worker left. If the remaining work was completed by the remaining workers in 14 days, then find the number of workers left after 8 days from the start of the work?
    
    
    10
    15
    20
    12
    11
    Option A
    Total work = workers*days
    
    Total units of work = 35*18 = 630 work
    
    Work done in 8 days = 35*8 = 280 work
    
    Remaining work = 630 – 280 = 350 work
    
    Let the number of workers left after 8 days be x,
    
    According to the question,
    
    350 / 14 = 35 – x
    
    25 = 35 – x
    
    x = 10
    
    After 8 days from the start of the work, 10 worker left the job.