Problems on time and work Part 1

Problems on time and work Part 1

  1. Work from Days:
    If A can do a piece of work in n days, then A's 1 day's work =1.
    n
  2. Days from Work:
    If A's 1 day's work =1,then A can finish the work in n days.
    n
  3. Ratio:
    If A is thrice as good a workman as B, then:
    Ratio of work done by A and B = 3 : 1.
    Ratio of times taken by A and B to finish a work = 1 : 3.

1. 
A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
A.
1
4
B.
1
10
C.
7
15
D.
8
15
Answer: Option D
Explanation:
A's 1 day's work =1;
15
B's 1 day's work =1;
20
(A + B)'s 1 day's work =(1+1)=7.
152060
(A + B)'s 4 day's work =(7x 4)=7.
6015
Therefore, Remaining work =(1 -7)=8.
1515
2. 
A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
A.
91days
5
B.
92days
5
C.
93days
5
D.10
Answer: Option C
Explanation:
(A + B + C)'s 1 day's work =1,
4
A's 1 day's work =1,
16
B's 1 day's work =1.
12
Therefore C's 1 day's work =1-(1+1)=(1-7)=5.
4161244848
So, C alone can do the work in48= 93days.
55
3. 
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
A.12 days
B.15 days
C.16 days
D.18 days
Answer: Option B
Explanation:
A's 2 day's work =1x 2=1.
2010
(A + B + C)'s 1 day's work =1+1+1=6=1.
2030606010
Work done in 3 days =1+1=1.
10105
Now,1work is done in 3 days.
5
 Whole work will be done in (3 x 5) = 15 days.
4. 
A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
A.20 days
B.
221days
2
C.25 days
D.30 days
Answer: Option B
Explanation:
Ratio of times taken by A and B = 1 : 3.
The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.
If difference of time is 2 days, B takes 3 days.
If difference of time is 60 days, B takes3x 60= 90 days.
2
So, A takes 30 days to do the work.
A's 1 day's work =1
30
B's 1 day's work =1
90
(A + B)'s 1 day's work =1+1=4=2
30909045
 A and B together can do the work in45= 221days.
22
5. 
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
A.Rs. 375
B.Rs. 400
C.Rs. 600
D.Rs. 800
Answer: Option B
Explanation:
C's 1 day's work =1-1+1=1-7=1.
36832424
A's wages : B's wages : C's wages =1:1:1= 4 : 3 : 1.
6824
C's share (for 3 days) = Rs.3 x1x 3200= Rs. 400.
24
6. 
If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
A.4 days
B.5 days
C.6 days
D.7 days
Answer: Option A
Explanation:
Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.
Then, 6x + 8y =1and 26x + 48y =1.
102
Solving these two equations, we get : x =1and y =1.
100200
(15 men + 20 boy)'s 1 day's work =15+20=1.
1002004
 15 men and 20 boys can do the work in 4 days.
7. 
A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
A.8 hours
B.10 hours
C.12 hours
D.24 hours
Answer: Option C
Explanation:
A's 1 hour's work =1;
4
(B + C)'s 1 hour's work =1;
3
(A + C)'s 1 hour's work =1.
2
(A + B + C)'s 1 hour's work =(1+1)=7.
4312
B's 1 hour's work =(7-1)=1.
12212
Therefore B alone will take 12 hours to do the work.
8. 
A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:
A.15 days
B.20 days
C.25 days
D.30 days
Answer: Option C
Explanation:
(A + B)'s 1 day's work =1
10
C's 1 day's work =1
50
(A + B + C)'s 1 day's work =1+1=6=3. .... (i)
10505025
A's 1 day's work = (B + C)'s 1 day's work .... (ii)
From (i) and (ii), we get: 2 x (A's 1 day's work) =3
25
 A's 1 day's work =3.
50
 B's 1 day's work1-3=2=1.
10505025
So, B alone could do the work in 25 days.
9. 
A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
A.23 days
B.37 days
C.371/2
D.40 days
Answer: Option C
Explanation:
Whole work is done by A in(20 x5)= 25 days.
4
Now,(1 -4)i.e.,1work is done by A and B in 3 days.
55
Whole work will be done by A and B in (3 x 5) = 15 days.
A's 1 day's work =1, (A + B)'s 1 day's work =1.
2515
Therefore B's 1 day's work =(1-1)=4=2.
152515075
So, B alone would do the work in75= 371days.
22
10. 
A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?
A.11:30 A.M.
B.12 noon
C.12:30 P.M.
D.1:00 P.M.
Answer: Option D
Explanation:
(P + Q + R)'s 1 hour's work =(1+1+1)=37.
81012120
Work done by P, Q and R in 2 hours =(37x 2)=37.
12060
Remaining work =(1 -37)=23.
6060
(Q + R)'s 1 hour's work =(1+1)=11.
101260
Now,11work is done by Q and R in 1 hour.
60
So,23work will be done by Q and R in(60x23)=23hours = 2 hours.
60116011
So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.

11. 
A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
A.5
B.
51
2
C.6
D.8
Answer: Option C
Explanation:
B's 10 day's work =(1x 10)=2.
153
Remaining work =(1 -2)=1.
33
Now,1work is done by A in 1 day.
18
Therefore1work is done by A in(18 x1)= 6 days.
33
12. 
4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
A.35
B.40
C.45
D.50
Answer: Option B
Explanation:
Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.
Then, 4x + 6y =1and 3x + 7y =1.
810
Solving the two equations, we get: x =11y =1
400400
 1 woman's 1 day's work =1.
400
 10 women's 1 day's work =1x 10=1.
40040
Hence, 10 women will complete the work in 40 days.
13. 
A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?
A.40
B.50
C.54
D.60
Answer: Option D
Explanation:
(A + B)'s 20 day's work =(1x 20)=2.
303
Remaining work =(1 -2)=1.
33
Now,1work is done by A in 20 days.
3
Therefore, the whole work will be done by A in (20 x 3) = 60 days.
14. 
P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?
A.
55
11
B.
56
11
C.
65
11
D.
66
11
Answer: Option A
Explanation:
P can complete the work in (12 x 8) hrs. = 96 hrs.
Q can complete the work in (8 x 10) hrs. = 80 hrs.
 P's1 hour's work =1and Q's 1 hour's work =1.
9680
(P + Q)'s 1 hour's work =1+1=11.
9680480
So, both P and Q will finish the work in480hrs.
11
 Number of days of 8 hours each =480x1=60days = 55days.
1181111
15. 
10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
A.3
B.5
C.7
D.Cannot be determined
E.None of these
Answer: Option C
Explanation:
1 woman's 1 day's work =1
70
1 child's 1 day's work =1
140
(5 women + 10 children)'s day's work =5+10=1+1=1
7014014147
 5 women and 10 children will complete the work in 7 days.

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