Problems on Time and Work Part 2

Problems on Time and Work Part 2

16. 
X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
A.6 days
B.10 days
C.15 days
D.20 days
Answer: Option B
Explanation:
Work done by X in 4 days =1x 4=1.
205
Remaining work =1 -1=4.
55
(X + Y)'s 1 day's work =1+1=8=2.
20126015
Now,2work is done by X and Y in 1 day.
15
So,4work will be done by X and Y in15x4= 6 days.
525
Hence, total time taken = (6 + 4) days = 10 days.
17. 
A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
A.11 days
B.13 days
C.
203days
17
D.None of these
Answer: Option B
Explanation:
Ratio of times taken by A and B = 100 : 130 = 10 : 13.
Suppose B takes x days to do the work.
Then, 10 : 13 :: 23 : x     =>     x =(23 x 13)    =>     x =299.
1010
A's 1 day's work =1;
23
B's 1 day's work =10.
299
(A + B)'s 1 day's work =(1+10)=23=1.
2329929913
Therefore, A and B together can complete the work in 13 days.
18. 
Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
A.7 hours 30 minutes
B.8 hours
C.8 hours 15 minutes
D.8 hours 25 minutes
Answer: Option C
Explanation:
Number of pages typed by Ravi in 1 hour =32=16.
63
Number of pages typed by Kumar in 1 hour =40= 8.
5
Number of pages typed by both in 1 hour =(16+ 8)=40.
33
Therefore Time taken by both to type 110 pages =(110 x3)hours
40
= 81hours (or) 8 hours 15 minutes.
4
19. 
A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:
A.
1day
24
B.
7day
24
C.
33days
7
D.4 days
Answer: Option C
Explanation:
Formula: If A can do a piece of work in n days, then A's 1 day's work =1.
n
(A + B + C)'s 1 day's work =1+1+1=7.
2461224
Formula: If A's 1 day's work =1,then A can finish the work in n days.
n
So, all the three together will complete the job in24 days=33days.
77
20. 
Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:
A.15
B.16
C.18
D.25
Answer: Option B
Explanation:
Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.
Suppose Tanya takes x days to do the work.
5 : 4 :: 20 : x     x =4 x 20
5
 x = 16 days.
Hence, Tanya takes 16 days to complete the work.

21. 
A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:
A.4 days
B.6 days
C.8 days
D.12 days
Answer: Option B
Explanation:
Suppose A, B and C take x,xandxdays respectively to finish the work.
23
Then,1+2+3=1
xxx2
6=1
x2
 x = 12.
So, B takes (12/2) = 6 days to finish the work.
22. 
A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :
A.8 days
B.10 days
C.12 days
D.15 days
Answer: Option C
Explanation:
(A + B)'s 1 day's work =(1+1)=1.
15106
Work done by A and B in 2 days =(1x 2)=1.
63
Remaining work =(1 -1)=2.
33
Now,1work is done by A in 1 day.
15
Therefore2work will be done by a in(15 x2)= 10 days.
33
Hence, the total time taken = (10 + 2) = 12 days.
23. 
A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
A.18 days
B.24 days
C.30 days
D.36 days
Answer: Option A
Explanation:
2(A + B + C)'s 1 day's work =(1+1+1)=15=1.
3024201208
Therefore, (A + B + C)'s 1 day's work =1=1.
2 x 816
Work done by A, B, C in 10 days =10=5.
168
Remaining work =(1 -5)=3.
88
A's 1 day's work =(1-1)=1.
162448
Now,1work is done by A in 1 day.
48
So,3work will be done by A in(48 x3)= 18 days.
88
24. 
A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :
A.4 days
B.6 days
C.8 days
D.18 days
Answer: Option A
Explanation:
Ratio of rates of working of A and B = 2 : 1.
So, ratio of times taken = 1 : 2.
B's 1 day's work =1.
12
Therefore A's 1 day's work =1; (2 times of B's work)
6
(A + B)'s 1 day's work =(1+1)=3=1.
612124
So, A and B together can finish the work in 4 days.
25. 
Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?
A.3 : 4
B.4 : 3
C.5 : 3
D.Data inadequate
Answer: Option B
Explanation:
(20 x 16) women can complete the work in 1 day.
 1 woman's 1 day's work =1.
320
(16 x 15) men can complete the work in 1 day.
 1 man's 1 day's work =1
240
So, required ratio
=1:1
240320
=1:1
34
= 4 : 3 (cross multiplied)
26. 
A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :
A.4 days
B.6 days
C.8 days
D.12 days
Answer: Option C
Explanation:
(A + B + C)'s 1 day's work =1;
6
(A + B)'s 1 day's work =1;
8
(B + C)'s 1 day's work =1.
12
Therefore (A + C)'s 1 day's work
=(2 x1)-(1+1)
6812
=(1-5(
324
=3
24
=1.
8
So, A and C together will do the work in 8 days.
27. 
A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:
A.5 days
B.6 days
C.10 days
D.
101days
2
Answer: Option C
Explanation:
(B + C)'s 1 day's work =1+1=7.
91236
Work done by B and C in 3 days =7x 3=7.
3612
Remaining work =1 -7=5.
1212
Now,1work is done by A in 1 day.
24
So,5work is done by A in24 x5= 10 days.
1212
28. 
X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?
A.
131days
3
B.15 days
C.20 days
D.26 days
Answer: Option A
Explanation:
Work done by X in 8 days =(1x 8)=1.
405
Remaining work =(1 -1)=4.
55
Now,4work is done by Y in 16 days.
5
Whole work will be done by Y in(16 x5)= 20 days.
4
Therefore X's 1 day's work =1, Y's 1 day's work =1.
4020
(X + Y)'s 1 day's work =(1+1)=3.
402040
Hence, X and Y will together complete the work in(40)= 131days.
33
29. 
A and B can do a job together in 7 days. A is 13/4 times as efficient as B. The same job can be done by A alone in :
A.
91days
3
B.11 days
C.
121days
4
D.
161days
3
Answer: Option B
Explanation:
(A's 1 day's work) : (B's 1 day's work) =7: 1   =   7 : 4.
4
Let A's and B's 1 day's work be 7x and 4x respectively.
Then, 7x + 4x =1    =>     11x =1    =>     x =1.
7777
Therefore A's 1 day's work =(1x 7)=1.
7711
30. 
A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
A.30 days
B.40 days
C.60 days
D.70 days
Answer: Option C
Explanation:
Let A's 1 day's work = x and B's 1 day's work = y.
Then, x + y =1and 16x + 44y = 1.
30
Solving these two equations, we get: x =1and y =1
6060
 B's 1 day's work =1.
60
Hence, B alone shall finish the whole work in 60 days.

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