Quantitative Aptitude: Time and Work Set 20

1. A work is to be completed in 40 days and 110 men were set to work, each working 8 hours a day. After 30 days, 4/5 of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 10 hours a day?
   
   
   44
   34
   54
   64
   74
   Option A
   30 * 110* 8 / 4/5 = 10 * x* 10 / 1/5
   =>x= 66
   more men required= 110-66 =44
   
    



2. Two pipes 1 and 2 can fill a tank in 10 hours and 30 hours respectively while a third pipe can empty the full tank in 25 hours. All the three pipes are opened in the beginning. After 15 hours, third pipe is closed. In how much time, will the tank be full?
   
   
   12 hours 45 min
   16 hours 45 min
   11 hours 45 min
   16 hours 35 min
   10 hours 45 min
   Option B
   
   Total work
   1---- 10
   2----- 30
   total----300
   3----- (-25)
   So third pipe 1 hour work = 300/-25 = -12
   Tank filled in 1 hour = 10+30 -12= 23
   So work done in 10 hours= 230
   Remaing work = 300-230 =70
   70 work will be done by 1 and 2 in 70/ ( 10+30)= 1.75= 105 min= 1 hr 45 min
   so work gets completed in 15+1 h 45m = 16 hours 45 min
   
    



3. 
   A worker was paid Rs. 1700per day for 30 days. but he was absent for 4 days and Rs. 15 was taken as penalty per day for absence. He was paid the full salary only for 18 days as he came late on the other days. Those who came late were given only half the salary for that day. What was the total salary paid per month to a worker who came on time everyday and was never absent?
   
   Rs.2400
   Rs.1200
   Rs.1000
   Rs.2500
   Rs.3000
   Option A
   Let the each day salary = Rs. x
   Then 18x + 8*x/2 - 60 = 1700
   =>x= 1700/22
   So monthly salary = 1700/22 * 30 = Rs.2400
   
    



4. Person A can do a piece of work in 10 days and person B can do it in 12 days. They work together for 3 days. Then person B leaves and A alone continues. 2 days after that C joins and the work is completed in 2 days. In how many days can C do it, if he works alone?
   
   
   20
   30
   40
   50
   60
   Option C
   Total work efficiency
   A 10 6
   60
   B 12 5
   
   3 days of A+B work = 11* 3 =33
   Remaining work = 60-33 = 27
   2 days of A work = 2* 6=12
   2* efficiency of A + 2 * efficiency of C = 15
   2*6 + 2*C = 15
   =>C= 3/2
   So C will complete the whole work in 60/3/2 = 40 days
   
    



5. Two men undertake to do a piece of work for Rs. 1200. One alone could do it in 12 days and the other in 16 days. With the assistance of a boy, they finish it in 6 days. The boy’s share should be-
   
   rs.150
   Rs. 200
   Rs.225
   Rs.300
   Rs.210
   Option A
   Ratio of efficiency = 24/12: 24/16 :24/ 6 - ( 24/12 + 24/16)
   = 4:3:1
   so boy's share = 1/ ( 4+3+1) * 1200 = Rs.150
   
    



6. Arun can do as much work in 4 days as lalitha can do in 5, and lalitha can do as much work in 6 days as suma in 7 days. In what time will suma do a piece of work which Arun can do in a week?
   
   
   12 5/ 24 days
   10 5/ 24 days
   11 5/ 24 days
   13 5/ 24 days
   14 5/ 24 days
   Option B
   arun * 4 = |Lalitha * 5
   Arun: Lalitha= 5:4
   Similarly lalitha : Suma= 7:6
   So Arun : Lalitha: Suma=35:28:24
   so efficiency of Arun= 35
   Work done in 7 days by arun = 7* 35= 245
   Suma will do 245 work in = 245/24 = 10 5/ 24 days
   
    



7. The work done by 8 men in 24 days is equal to the work done by 12 women in 20 days and is also equal to the work done by 16 children in 18 days. A man, a woman and a child working together take 20 days to complete a particular job. In how many days will the same job be completed by 4 women and 10 children working together?
   
   
   2
   7
   4
   5
   6
   Option D
   8 M * 24 = 12w * 20
   M = 5W/4
   12W * 20 = 16C * 18
   W= 6C/5
   1M+ 1W +1C= 5w/4 + W + 5W/6 = 37W/12
   2W+ 5C= 2W+ 5*5W/6 =37W/6
   M1*D1=M2*D2
   37/12 *10 = 37/6 * Days
   days= 5
   
    



8. Akil, Bindhu and Jay can do a job in 20, 30 and 40 days respectively. The three started the job together; Akil left the job 4 days before it was completed and Bindhu left the job 3 days before it was completed. In how many days was the job completed?
   
   
   12
   11
   15
   14
   17
   Option A
   Total work efficiency
   Akil-> 20 6
   Bindhu-> 30 120 4
   Jay -> 40 3
   Let them completed the work in x days.
   6( x-4) + 4( x-3) + 3x= 120
   => x= 12 days
   
    



9. 2 and 3 are equally efficient, but the efficiency of 1 is half of each 2 and 3. 1 and 2 started a work and 3 days later 3 joined them. If 1 alone can do the work in 14 days, then in how many more days the work will be completed?
   
   
   5
   3
   4
   1
   2
   Option D
   efficiency --> 1:2 = 1:2
   efficiency---> 2:3 = 1:1
   1:2:3 = 1:2:2
   days = 1: 1/2: 1/2 ( days inversly proportional to efficiency)
   total work efficiency
   1--> 14 days 14 1
   2---> 7 days 2
   3---> 7 days 2
   Work done by 1& 2 in 3 days= 3*3= 9
   remaining work = 14-9 =5
   time taken by 1 and 2 and 3 to finish 5 works = 5/5 =1
   so more days required= 1
   
    



10. person 1 and 2 can do a work in 20 and 25 days respectively. After doing collectively 10 days of work, they leave the work due to illness and person 3 completes rest of the work in 3 days. How many days person3 alone can take to complete the whole work?
    
    
    20
    21
    33
    49
    30
    Option E
    work efficiency
    person 1-->20 5
    100
    person 2--->25 4
    work completed by person 1 and 2 in 10 days= 9*10 = 90 work
    remaining work = 100-90 = 10
    10 work done by person 3 in 3 days.
    so efficiency 10/3
    So person 3 can complete in 100/ 10/3 = 30 days