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Q #26
⏰ :

Directions: Read the following information to answer the question.

Two workers A and B are engaged to do a work. A working alone takes 8 hours more to Complete the job than if both worked together. If B worked alone, he would need 9/2 hours more to complete the job than they both working together. What time would they take to do the work together?

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Explanation :

 Let A and B together take x hours to complete the work. Then,

 A alone takes (x + 8) hrs and B alone takes x +9/2  hrs to complete the work, Then,     

1/(x + 8)+1/{x +    9/2}=1/x

 1/(x + 8)+2/(2x + 9)=1/x

 x (4x + 25) = (x + 8) (2x + 9)             

 2x2 = 72     

  x^2 = 36     

  x = 6.   


Q #27
⏰ :

Directions: Read the following information to answer the question.

A and B can do a piece of work in 72 days; B and C can do it in 120 days; A and C can do it in 90 days. In what time can A alone do it?

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Explanation :

 (A + B)'s 1 day's work =    1/72

 (B + C)'s 1 day's work =    1/120

 ; (A + C)'s 1 day's work =1/90

 Adding, we get: 2(A + B + C)’s 1 day’s work =1/72+1/120+1/90=12/360=1/30

 (A + B + C)'s 1 day's work =1/60

 So, A’s 1 day’s work =1/60-1/120 =1/120

  A alone can do that work in 120 days.   


Q #28
⏰ :

Directions: Read the following information to answer the question.

Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked1/3 as efficiently as he actually did, the work would have been completed in 3 days. A alone could complete the work in:

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Explanation :

 Let A’s 1 day’s work = x and B’s 1 day’s work = y.

 Then, x + y =1/5and 2x +1/3

 y =1/3

 Solving, we get : x =4/25

and y =    1/25

A's 1 day's work =4/25

 So, A alone could complete the work in    25/4days


Q #29
⏰ :

Directions: Read the following information to answer the question.

A and B can together finish a work in 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 job?

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Explanation :

 (A + B)'s 20 days' work ={1/30} x 20=2/3

. Remaining work =1 -2/3=1/3

 Now,1/3

  work is done by A in 20 days.             

 Whole work will be done by A in (20 x 3) = 60 days.


Q #30
⏰ :

Directions: Read the following information to answer the question.

A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was:

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Explanation :

 

(A + B)’s 1 day’s work =    1/45+    1/40

 =17/360

 Work done by B in 23 days ={1/40} x 23    =23/40

. Remaining work =1 -23/40

 =17/40

 Now,    17/360 Work was done by (A + B) in 1 day.         

17/40work was done by (A + B) in1 x{360/17}x17/40

  = 9 days.     

  A left after 9 days.