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