Time and work

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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 x 1 ) – ( 1 + 1 )
6 8 12
= ( 1 – 5 (
3 24
= 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.
10 1 days
2

Answer: Option C

Explanation:

 

 

(B + C)’s 1 day’s work = 1 + 1 = 7 .
9 12 36

 

Work done by B and C in 3 days = 7 x 3 = 7 .
36 12

 

Remaining work = 1 – 7 = 5 .
12 12

 

Now, 1 work is done by A in 1 day.
24

 

So, 5 work is done by A in 24 x 5 = 10 days.
12 12
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.  

13 1 days
3
B. 15 days
C. 20 days D. 26 days

Answer: Option A

Explanation:

 

 

Work done by X in 8 days = ( 1 x 8 ) = 1 .
40 5

 

Remaining work = ( 1 – 1 ) = 4 .
5 5

 

Now, 4 work is done by Y in 16 days.
5

 

Whole work will be done by Y in ( 16 x 5 ) = 20 days.
4

 

Therefore X’s 1 day’s work = 1 , Y’s 1 day’s work = 1 .
40 20

 

(X + Y)’s 1 day’s work = ( 1 + 1 ) = 3 .
40 20 40

 

Hence, X and Y will together complete the work in ( 40 ) = 13 1 days.
3 3
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.  

9 1 days
3
B. 11 days
C.  

12 1 days
4
D.  

16 1 days
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 .
7 7 77

 

Therefore A’s 1 day’s work = ( 1 x 7 ) = 1 .
77 11
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 = 1 and 16x + 44y = 1.
30

 

Solving these two equations, we get: x = 1 and y = 1
60 60

 

B’s 1 day’s work = 1 .
60

Hence, B alone shall finish the whole work in 60 days.
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