Simpler logical solution pls :)

Is Option E is the answer ?

[spoiler]yep [/spoiler]

Simpler logical solution pls

Himu,
I Obtained just by substituting answers (A,D and then E)
Even I dont know Simpler Logical Solution

himu wrote:It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages?

5

6

8

10

12

Since Tom and Jack type 25 pages in 3 hours, their combined rate = pages/time = 25/3 pages per hour.

We can plug in the answers, which represent the number of hours for Jack to type 40 pages:
5, 6, 8, 10, 12
It will take Jack HALF as long to type 20 pages:
2.5, 3, 4, 5, 6
Since Tom takes 2 FEWER hours to type 20 pages, the options for Tom's time to type 20 pages are as follows:
.5, 1, 2, 3, 4

When the correct answer choice is plugged in, the combined rate for Jack and Tom will be 25/3 pages per hour.

Answer choice C:
Jack's rate = pages/time = 20/4 = 5.
Tom's rate = pages/time = 20/2 = 10.
Combined rate = 5+10 = 15 pages per hour.
Since the required combined rate is 25/3 pages per hour -- about HALF as fast -- Jack and Tom must work much MORE SLOWLY.
Thus, they each must take MUCH LONGER to type 20 pages.

Answer choice E:
Jack's rate = pages/time = 20/6 = 10/3 page per hour.
Tom's rate = pages/time = 20/4 = 5 pages per hour.
Combined rate = 10/3 + 5 = 10/3 + 15/3 = 25/3 pages per hour.
Success!

The correct answer is E.

See the below approach seems logical to you:

Let rate of Jack be j and that of Tom be t. Also let T be the # hours that Tom takes to type 20 pages.

From given info:

t*T=20 and j*(T+2)=20;

Also, (j+t)*3=25 => j+t=25/3

Now, the problem asks time it will take for Jack to type 40 pages i.e. double # pages to type. Assuming that Jack works at same rate, Jack will take 2*(T+2) to type 40 pages.

So using above 3 equations, we will have the answer as follows:
(20/T) + (20/T+2) = 25/3 i.e. (4/T) + 4/(T+2)= 5/3
solving above we have T=4

Hence, time taken by Jack to type 40 pages =2*(T+2)=2*6=12;

Hope this helps!!

Answer is 12

himu wrote:It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages?

5

6

8

10

12

We can let Tom’s rate = 20/x and Jack’s rate = 20/(x+2), and their combined rate is 25/3; thus:

20/x + 20/(x+2) = 25/3

Multiplying by 3x(x+2), we have:

20(3)(x + 2) + 20(3x) = 25(x)(x + 2)

60x + 120 + 60x = 25x^2 + 50x

25^x - 70x - 120 = 0

5x^2 - 14x - 24 = 0

(5x + 6)(x - 4) = 0

x = -5/6 or x = 4

Since x can’t be negative, we see that x must be 4, so Jack's rate is 20/6 = 10/3.

So it takes him 40/(10/3) = 120/10 = 12 hours to type 40 pages.

Alternate Solution:

Let’s pick a common multiple of 20, 25 and 40, such as 200, and calculate the number of hours to type that number of pages for each scenario.

Since Jack takes 2 more hours than Tom to type 20 pages, it will take Jack 20 more hours than Tom to type 200 pages.

Since Jack and Tom working together can type 25 pages in 3 hours, they can type 200 pages in 12 hours.

Let’s denote the number of hours for Tom to type 200 pages by t. Then, in one hour, Tom can complete 1/t of the job. Since Jack takes 20 more hours than Tom to do the same job, it will take him t + 20 hours to type 200 pages and he can complete 1/(t + 20) of the job in one hour. Working together, they can complete the same job (200 pages) in 24 hours; thus in one hour, they complete 1/24 of the job. We can create the following equation:

1/t + 1/(t + 20) = 1/24

Let’s multiply each side by 24t(t + 20):

24(t + 20) + 24t = t(t + 20)

24t + 480 + 24t = t^2 + 20t

t^2 - 28t - 480 = 0

(t - 40)(t + 12) = 0

t = 40 or t = -12

Since t cannot be negative, t must equal 40. Since it takes Tom 40 hours to type 200 pages, it will take him 1/5 the number of hours to type 1/5 the number of pages (40 pages); thus Tom will type 40 pages in 40 x 1/5 = 12 hours.

Answer: E