Brain Teasers and Puzzles 

Workings

Hint
Look at the last letters.

Answer
Steve.

The last letters are in alphabetical order.

Workings

Hint
A little algebra might help.

Answer
¹/₈.

Reasoning
If we convert the question to algebra, we have:
((n^2 + 4) x 2 – 3) x 4 – n = 20

Expanding the brackets and simplifying gives:

(2n^2 + 8 – 3) x 4 – n = 20

    (2n^2 + 5) x 4 – n = 20

         8n^2 + 20 – n = 20

              8n^2 – n = 0 (*)

                8n – 1 = 0

                    8n = 1

                     n = ¹/₈

In the equation marked (*) zero is also a potential solution, but as the question tells us that we "Start with a number larger than 0" we know that n can't be 0, and therefore we can safely divide by n.

Double-Checking
                 ¹/₈
   squared     = ¹/₆₄
   add 4       = 4¹/₆₄
   double      = 8¹/₃₂
   take away 3 = 5¹/₃₂
   times 4     = 20¹/₈

   subtracting ¹/₈ gives 20, as required.

Workings

Hint

Answer
 

Workings

Hint
One of the words is Railway.

Answer
Railway, rainbow, recycle, replace, respect, royalty, referee, rejoice.