Quantitative Aptitude: Time and Work Set 24

1. A can do a piece of work in 10 days and B can do a piece of work in 15 days, then how many days together complete the same piece of work ?
   6days
   8days
   4days
   2days
   none of this
   Option A
   solution: xy/x+y
   10*15/10+15 = 6days

    

2. P and Q alone can do a piece of work in x hours and (x+10) hours respectively. If both P and Q together can do same piece of work in 12 hours, then find the time taken by P alone to do the same work is what percent of that of Q alone ?
   100/3%
   200/3%
   220/3%
   95/3%
   none of these
   Option B
   solution: [x*(x+10)]/[x+(x+10)] = 12
   x^2+10x = 24x+120
   x^2-14x-120 = 0
   x=20,-6
   x= 20 hours
   P=20 hours
   Q=30 hours
   %=20/30*100=200/3%
   

    

3. 10 men or 30 boys can do any work in 12 days, then time taken to complete the same work by 10 men and 15 boys .
   8 days
   4 days
   2 days
   5 days
   none of this
   Option A
   solution: 12/(10/10+15/30)= 12/(1+1/2)
   =12*2/3 =8 days

    

4. Sunil can do a work in 12 days and Ravi can do same work in 8 days . If they work toghether for 2 days, then B left the work and remaining work done by A, then how many days total work will be completed.
   9
   12
   10
   14
   18
   Option A
   Sunil can do a work = 12 days
   Ravi can do a work=8 days
   Total work = LCM of 12 and 8=48 work
   efficiency of Sunil = 48/12 = 4 work
   efficiency of Ravi = 48/8 =6 work
   toghether work for 2days = (6+4)*2= 20work
   remain work done by Sunil = 28/4= 7days
   total work completed = 7+2 =9 days

    

5. Sinu and Rinu can do a work 20 days and 30 days respctively . If they got rs.1500 wages in total, then find share of Rinu .
   600
   1200
   800
   1000
   none of these
   Option A
   Total work = LCM of (20 and 30)
   total work = 60
   efficiency of Sinu = 60/20 =3 work/day
   efficiency of Rinu=60/30=2 work/days
   wages of Rinu = 1500*2/5 =rs.600

    

6. X,Y and Z completed a work costing rs.1800 . X work for 6 days , Y worked for 4 days and Z worked for 9 days . If their daily wages are in the ratio of 5:6:4, then how much amount will be received by X ?
   600
   500
   400
   200
   none of this
   Option A
   Ratio of the wages of A, B and C = 5:6:4
   X share: Y share : Z share
   =(6*5) : (4*6) : (9*4)
   =30 : 24 : 36 =5:4:6
   X’s share = 5/15*1800 = rs.600

    

7. A & B working together completes work in 24 days while B & C completes the same work in 30 days. If C is 20% more efficient than B, then in how many days working alone A will complete the half of the work ?
   122/7 days
   112/7 days
   119/9 days
   132/7 days
   130/7 days
   Option D
   LCM of 24 & 30=120
   efficiency of A&B working together=5
   efficiency of B&C working together=4
   ATQ, efficiency of C 20% more than B
   ratio of efficiency of B&C =5:6
   balancing both sides b multiplyng by 11
   efficiency of B&C working together =44
   efficiency of A&B working together=55
   efficiency of B=5/11*44=20
   efficiency of A=35
   A alone can do half of work=(120*11)/(2*35)=132/7 days
   

    

8. 12 men can complete a piece of work in 36 days. 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20days. If only women were to complete the remaining in 4 days, how many women would be required ?
   35
   30
   45
   40
   50
   Option B
   solution: 12 men*36days=18women*60days
   2men=5women
   8men=20women
   total work=18*60=1080 work
   (20women+20women) is working for 20days
   work completed=40women*20days=800work
   remaining work=1080-800=280 work
   women required=280/4=70 women
   extra women required=70-40=30 women

    

9. Some persons can built a bridge in 100 days, but 25 persons do not join the group to complete the bridge so the work is finished in 150 days. Find out how many persons worked initially ?
   80
   75
   85
   92
   none of these
   Option B
   solution: let total no. of person have in the group initially=x
   total work=100*x
   100*x=(x-25)*150
   x=75
   

    

10. P, Q, R & S can do a work individually in 10, 20, 30 & 40 days respectively. P & Q can do half of the work and the remaining half is done by R & S together. In how many days was the work finished ?
    260/11 days
    245/11 days
    270/11 days
    250/21 days
    280/21 days
    Option D
    solution: LCM of 10, 20, 30, 40=120
    total work=120
    efficiency of P=120/10=12
    efficiency of Q=120/20=6
    efficiency of R=120/30=3
    half the work done by P & Q=60/18=10/3 days
    remaining half work done by R & S= 60/7 days
    total days required=10/3+60/7=250/21days

     

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