# Quantitative Aptitude: Time and Work Set 16

1. P and Q clean the room in 18 hours and 15 hours resp. If P works for 3 hours and Q works for the remaining time only, then in how many hours would Q complete the remaining work?
10(1/2) hours
13(1/4) hours
10(1/5) hours
12(1/2) hours
11(1/3) hours
Option D
Work done in first 3 hours = 3*1/18 = 1/6
Remaining work = 1 – 1/6 = 5/6
Work completed by Q in 5/6/1/15 = 12(1/2) hours

2. A and B together, B and C together and A and C together can complete the work in 35 days, 42 days and 30 days resp. C is how much percent less/more efficient than A ?
22%
25%
35%
30%
20%
Option B
Total work (LCM of 35,42 and 30) = 210 units
Amount of work done by A, B and C together in one day = (6+5+7)/2 = 9 units
Amount of work done by A alone in one day = 9-5 = 4 days
Amount of work done by B alone in one day = 9-6 = 3 days
Required% = (4-3)/4*100 = 25%

3. A can do a work in 24 hours while B can do the work in 18 hours. Efficiency of C is 500/7% more than that of A and B when working together then find out the time taken by C alone to complete the work.
3 hours
6 hours
4 hours
8 hours
5 hours
Option B
Total work (LCM of 24 and 18) = 72 units
Work is done by A in one hour = 72/24 = 3 units
Work is done by B in one hour = 72/18 = 4 units
Work is completed by A and B together in one hour = 3+4 = 7 units
Number of units of work is completed by C in one hour = 7 + 71(3/7)% of 7 = 7+5 = 12 units
Required time taken by C alone to complete the work = 72/12 = 6 hours

4. A alone can do a work in 12 days but when A works with B, the work gets completed in 60/7 days. B and C together do the work in 12 days. In how many days can A and C together do the work?
6.6 days
8.1 days
7.5 days
4.2 days
5.5 days
Option C
Time taken by B alone to complete the task be x days. Time taken by C alone be y days. 1/12 + 1/x = 7/60
=> x = 30 1/30 + 1/y = 1/12
=> y = 20 Part of the work done by A and C together in a day = 1/12 + 1/20 = 8/60
Required number of days = 60/8 = 7.5 days

5. A and B can complete a task in 30 hours and 10 hours resp. Only A works during the first hour and both A and B work during the 2nd hour. If they continue working in this pattern. In how many hours would 41/60 of the work be completed?
7(1/5) hours
5(1/4) hours
6(1/3) hours
8(1/2) hours
7(1/3) hours
Option D
Work done in first 2 hours = 1/30 + (1/10 + 1/30)
= 1/6
Work done in first 8 hours = 4*1/6
Work left to be completed = 41/60 – 4/6 = 1/60
Number of hours taken to complete the work = 8(1/2) hours

6. Timon and Pumba are two friends. A total of Rs. 960 was paid to both of them for completing a work. Timon started working and worked for ‘x’ days and then left and the remaining work was completed by Pumba and he was paid Rs. 540. If Timon and Pumba alone can complete the work in 6 days and 12 days resp. find the value of x.
4.505 days
3.674 days
5.220 days
2.625 days
3.112 days
Option D
Total work (LCM of 6 and 12) = 12 units
Money paid to complete the total work = 960/12 = Rs. 80
Number of units of work completed by Pumba = 540/80 = 6.75 units
Number of units of work completed by Timon = 12 – 6.75 = 5.25 units
Number of days taken(x) to complete 5.25 units by Timon = 5.25/2 = 2.625 days

7. Sita, Gita and Rita can complete a work in 6, 10 and 15 days resp. Gita and Rita started the work together and worked for ‘x’ days and then both left the work and the remaining work is completed by Sita in 3 days. Find the value of x.
9 days
5 days
8 days
4 days
3 days
Option E
Total work (LCM of 6,10 and 15) = 30 units
Amount of work done by Sita, Gita and Rita in one day resp. = 5, 3 and 2 units
Amount of work done by Sita in 3 days = 5*3 = 15 days
Amount of work done by Gita and Rita together = 30 – 15 = 15 days
Amount of work done by Gita and Rita in one day = 3+2 = 5 days
Number of days worked by Gita and Rita together = 15/5 = 3 days

8. Ram is 20% less efficient than Amit and Deepak is 50% more efficient than Ram. If Amit, Ram and Deepak together can complete the work in 8 days, find the time taken by Amit and Deepak together to complete the work.
123/18 days
127/10 days
119/11 days
124/13 days
120/11 days
Option E
Let the time taken Ram alone to complete the work be ‘x’ days.
Time taken by Amit alone to complete the work = x*0.80 = 4x/5 days
Time taken by Deepka alone to complete the work = x/1.5 = 2x/3 days
1/x+5/4x+3/2x = 1/8
=> x = 30
Time taken by Amit and Deepak alone to complete the work = 4x/5 = 24 and 2x/3 = 20 resp.
Required time together by Amit and Deepak = 1/[(1/24)+(1/20)] = 120/11 days

9. X,Y and Z alone can do a certain piece of work in 42,30 and 35 days resp. They started working together but after ‘x’ days, Z left the job and ‘x’ days before completion of work Y also left the job. Find the value of ‘x’ if the whole work was completed in 3x days.
8
9
6
7
4
Option C
3x/42+2x/30+x/35 = 1
=> x/14 + x/15 + x/35 = 1
=> x = 6

10. A,B and C individually can do a certain piece of work in 35,42 and 24 days resp. They started working together but after ‘x’ days A and C left the job and the remaining work is completed by B with 25% more efficiency. If the whole work is completed in 114/5 days then find the value of x.
7
6
5
3
4
Option C
Total work (LCM of 35, 42 and 24) = 840 units
Amount of work done by A,B and C = 24 , 20 and 35 units
Amount of work done by A, B and C together in ‘x’ days
= (24+20+35)*x = 79x units
Amount of work done by B alone in one day after increased efficiency = 20*1.25 = 25 units
Amount of work done by B alone in {(114/5) – x} days with increased efficiency = {(114/5) – 5} * 25
= (570 – 25x) units
79x + 570 – 25x = 840
=> x = 5