Time and Work Practice Problems Set – 2

Time and Work Practice Problems Set – 2
1. A can do a work in 50 days and B in 40 days . They work together for 10 days. and then A leaves B to finish the work alone. How long will B take to finish it??
(a)  11 days
(b)  18 days
(c)  22 days
(d)  26 days
(e)  None of these
2. 30 men, working 4 hrs a day can do a piece of work in 10 days. Find the number of days in which 45 men working 8 hrs a day can do twice the work. Assume that 2 men of the first group do as much wrk in 2 hrs as 4 men of the second group do in 1 hr.
(a)  6(1/3) days
(b)  6(2/3) days
(c)  5(3/6) days
(d)  3(1/6) days
(e)  None of these
3. A alone would take 27 hrs more to complete the job than if both A and B would together. If B worked alone, he took 3 hrs more to complete the job than A and B worked together. What time, would they take if both A and B worked together?
(a)  8 hours
(b)  10 hours
(c)  9 hours
(d)  6 hours
(e)  None of these
4. A and B together can do a piece of work in 12 days which B and C together will do in 16 days. After A has been working on it for 5 days, and B for 7 days, C finishes it in 13 days. In how many days A,B and C alone will do the work ?
(a)  16, 48 and 26 days respectively
(b)  16, 48 and 24 days respectively
(c)  26, 48 and 24 days respectively
(d)  16, 46 and 24 days respectively
(e)  None of these
5. Two women Ganga and Jamuna, working separately can mow a field in 8 and 12 hours respectively. If they work for an hour alternately, Ganga beginning at 9 am, when will the mowing be finished?
(a)  9:30 PM
(b)  8:30 PM
(c)  6:00 AM
(d)  7:00 PM
(e)  None of these
6. A, B and C together can do a work in 12 days. A alone can do the work in 36 days and B alone can do the same work in 54 days. Find in what time C alone can do that work?
(a)  9 days
(b)  18 days
(c)  24 days
(d)  27 days
(e)  None of these
7. A, B and C together can do a work in 4 days. A alone can do the work in 12 days B alone can do the same work in 18 days. Find in what time C alone can do the same work alone?
(a)  9 days
(b)  18 days
(c)  27 days
(d)  8 days
(e)  None of these
8. A can complete a work in 35 days and B can do the same work in 28 days. If A after doing 10 days, leaves the work , find in how many days B will do the remaining work?
(a)  15 days
(b)  10 days
(c)  27 days
(d)  24 days
(e)  None of these
9. A can complete a work in 24 days and B can complete the same work in 18 days. If A after doing 4 days leaves the work find in how many days B will complete the remaining work?
(a)  11 days
(b)  15 days
(c)  12 days
(d)  10 days
(e)  None of these
10. A and B together can do a piece of work in 6 days, B alone could do it in 8 days. Supposing B works at it for 5 days, in how many days A alone could finish the remaining work?
(a)  9 days
(b)  8 days
(c)  24 days
(d)  12 days
(e)  None of these
11. A and B can do a piece of work in 20 days and 30 days. both starts the work together for some time, but B leaves the job 5 days before the work is completed. Find the time in which work is completed.
(a)  7 days
(b)  12 days
(c)  14 days
(d)  16 days
(e)  None of these

Solutions:
1. (c) 22 days
Let the total work be 200 work
Efficiency of
A = 200/50 = 4 work/day
B = 200/40 = 5 work/day
A+B’s efficiency = 9/day
A+B’s 10 days work = 9*10 = 90
Remaining work = 200-90 = 110
Time taken by B alone to finish the remaining wrk = 110/5 = 22days

2. (b) 6(2/3) days
M1D1H1E1W2 = M2D2H2E2W1 (From MDH Rule)
Efficiency of first grp : 2nd grp = 2*2 :4*1 = 1:1
Now, D2 = M1D1H1E1W2 / M2H2E2W1
D2 = 30*4*10*1*2 / 45*8*1*1
D2 = 20/3 = 6(2/3) days

3. (c) 9 Hours
Let A+B together takes X hours
A will take X+27 hrs
B will take X+3 hrs
Let the total work be (X+27)(X+3)
Efficiency of A= X+3
B = X+27
Total efficiency = 2X+30
Time working together = (X+27)(X+3) / 2X+30 = X
==> X^2 +30X + 81 = 2X^2 + 30X
or, X^2 = 81 or X= 9 hrs (neglecting –Ve time )

4.  (b) 16, 48 and 24 days respectively
Let the total work be 48
Efficiency of
A+B = 4/day…… (i)
B+C = 3/day……..(ii)
Now, A works for 5 days, B works for 7 days and C works for 13 days and completes the total work of 48.
This can be rewritten as
A+B for 5 days + B+C for 2 days + C for 11 days completes the total work of 48
Now, A+B’s 5 days work = 20
B+C’s 2 days work = 6
Therefore, 20+6+ C’s 11 days work = 48
C’s  11 days work = 48-26 = 22
C’s efficiency = 2/day.. (iii)
From (i),(ii),(iii)
C’s efficiency = 2
B’s Efficiency = 1
A’s efficiency = 3
Time taken by
A= 16 days, B= 48 days, and C= 24 days

5. (e) None of these (6:30PM)
Let the total work be 24
Efficiency of Ganga = 24/8 = 3/hr
Efficiency of Jamuna= 24/12 = 2/hr
They work alternately starting from Ganga
First 2 hrs work = 3+2 = 5
First 8 hrs work = 20
Remaining = 24-20 = 4
9th hr work to be done by Ganga = 3
Remaining work = 4-3 = 1 to be done by Jamuna in 1/2 hr.
Total time = 8+1+(1/2) hrs = 9.5 hrs or 9 Hr 30 minutes
So work will be completed by 9AM + 9 hrs 30 minutes = 18 hrs 30 minutes or 6:30 PM

6. (d) 27 Days
Let the total work be 108 (Common Multiple of 12,36 and 54)
Efficiency of A+B+C =108/12=  9,
of A alone = 108/36 = 3 and
of B alone = 108/54 = 2
Therefore of C alone = 9-(3+2) = 4
Time taken by C = 108/4 = 27 days

7. (a) 9 Days
Let the total work be 36 ( Can take any value Preferably Common Multiple )
Efficiency of
A+B+C = 36/4 = 9
A alone= 36/12 = 3
B alone = 36/18 = 2
C alone = A+B+C- (A+B) = 9-(3+2) = 4
Time taken by C alone = 36/4 = 9 days

8. (e) None of these (20 days)
Let the total work be 140
Efficiency of A = 4
Efficiency of B = 5
A works for 10 days = 4*10 = 40
Remaining work = 140-40 = 100 to be done by B
B will do it in 100/5 = 20 days

9. (b) 15 days
Let the total work be 72
Efficiency of A = 3 and Of B = 4
A’s 4 days work = 3*4 = 12 remaining work = 72 -12 = 60
Work completed by B in 60/4 = 15 days

10. (a) 9 days
Let the total work be 24
Efficiency of A+B = 4
Efficiency of B = 3
Efficiency of A = 1 as A+B = 4 and B= 3
Work done by B in 5 day = 3*5 = 15
Remaining work = 24-15 = 9
Remaining work to be done by A in 9/1 = 9 days

11. (c) 14 days
Let the total work be 60
Efficiency of A = 3 and of B = 2
Efficiency of A+B = 3+2 = 5
Suppose B never left the work then if the time taken remains same then work done by B in those 5 days will be added to original work.
Therefore, Now, works become = 60 + B’s 5 days work = 60+10 = 70
Time taken = 70/5 = 14 days

Other way :- B leaves the work 5 days before means A did work alone for that 5 days
Work Done by A in that 5 day = 5/20 = 1/4
Remaining work = 3/4
To complete the work together A+B would have taken  1/ (1/20+ 1/30)  = 600/50 = 12 days
3/4th of the work together will be completed in 12*3/4 = 9 days
Total time = 5+9 = 14 days