6.  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 4 1/2 hours more to complete the job than they both working together. what time would they take to do the work together?

6 hours
4 hours
5 hours
7 hours

```Answer

Answer: Option  A 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)
= 2x^2 = 72 = x^2 =36 = x =6. ```

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7.  Ronald and elan are working on assignment. Ronald takes 6 hours to type 32 pages on a computer, while elan 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?

7 hours 30 minutes
8 hours
8 hours 15 minutes
8 hours 25 minutes

```Answer

Answer: Option  C Explanation:Number of pages typed by Ronald in 1 hour = 32/6 = 16/3.
Number of pages typed by elan in 1 hour = 40/5 = 8.
Number of pages typed by both in 1 hour = (16/3 + 8) = 40/3.
therefore time taken by both to type 110 pages = (110*3/40) hrs = 8 hrs 15 min. ```

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8.  P,Q and R three typists who working simultaneously can type 216 pages in 4 hours.In one hour R can type as many pages more than Q as Q can type more than P.During a period of 5 hours R can type many pages as P can during 7 hours. How many pages does each of them type per hour?

14,17,20
15,17,22
15,18,21
16,18,22

```Answer

Answer: Option  C Explanation:Let the number of pages typed in one hour by P,Q, and R be x,y, and z respectively.
x+y+z = 216/4 = x+y+z = 54 .........(1)
z-y = y-x          = 2y = x+z     .........(2)
5z = 7x            = x = 5/7z      .........(3)
solving (1) (2) and (3) we get x = 15; y= 18 ; z = 21  ```

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9.  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?

5 6/11
6 5/11
5 5/11
6 6/11

```Answer

Answer: Option  C Explanation:P can complete the work in (12*8) hrs. = 96 hrs.                                                                                                                                                                     Q can complete the work in (8*10) hrs. = 80 hrs.
therefore P's 1 hour's work = 1/96 and  Q' s 1 hour's work = 1/80.
(P + Q)'s 1 hour' s work = ( 1/96 + 1/80) = 11/480.
so both P and Q will finish the work in (480/ 11) hrs.
therefore number of days of 8 hours each = (480/11*1/8) = 60/11 days = 5 5/11 days.
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10.  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

3 3/7 days
1/24 days
7/24 days
4 days

```Answer

Answer: Option  A Explanation:(A+B+C)'s 1 day's work = (1/24+ 1/6+ 1/12) = 7/24.
so A,B and C together will complete the job in 24/7 = 3 3/7 days. ```

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