Question

a number of three digits has the hundred digit four times the unit digit and the sum of the three digits is 14. If the three digits are written in reverse the value of the number is decreased by 594 ,find the number

Answer 1

If you express the 3-digit number as XYZ, then 
X = 4Z and 
X + Y + Z = 14 and 
(100X+10Y+Z) - (100Z+10Y+X) = 594. 

Take the last equation and add all of the numbers together. 
You will get 99X - 99Z = 594. (How did I get that final figure? Easy: It's 100X-X+10Y-10Y-100Z+Z = 594.) 
So then...if every X = 4Z, then the above equation can be expressed as 4(99Z) - 99Z = 594, or 396Z - 99Z = 594, or 297Z = 594. Solving for Z, you've got Z = 2. 
If Z = 2, then X must be 8 (because it's 4 times Z), and in order to get X+Y+Z=14, then Y must be 4. 
Therefore, the three-digit number is 842.

An alternate method:

In order for the hundreds digit to be four times the units digit, the number must be of the form: 
4?1 or 8?2 

Since the sum of the digits is 14, the answer could be: 
491 or 842 

However, the first choice isn't big enough to have a difference of 594 when reversed. 

The other number (842) does work. Let's verify that: 
842 - 248 = 594 

Answer: 
842

I have written another solution for this question here:
https://drive.google.com/file/d/0B93wLOqLZwn_UGt1WG1DNzA2S2s/edit

This answer has a more mathematical approach and I recommend uh to use it only if uh are intrested in higher mathematics ;)

Hope This Helps :)