Random Puzzles 

Workings

Hint
A little algebra might help.

Answer
He will be 35 in 14 years.

Reasoning
He is currently 21.

If X is his current age, then:
  X = 14 +  X
           ———
            3
so

   2X = 14
  ———
   3

and

  2X = 42

So

  X = 21

He is currently 21 and his favourite book is currently 14 years old, when it is 28 years old (double its age) he will be 35.

Workings

Hint
Find two numbers that multiply to 187.

Answer
There were 17 children, with 11 sweets each.

Reasoning
If we number the clues:
each child had more than one sweet there were more children than there were sweets per child
187 only has the factors 1, 11, 17, 187. Therefore, the only possible answers are:

   1 child, with 187 sweets each, which is not allowed by (2)

   11 children, with 17 sweets each, which is not allowed by (2)

   17 children, with 11 sweets each (*)

   187 children, with 1 sweet each, which is not allowed by (1)

Only one possible answer (*) isn't eliminated.

Workings

Hint
The first letters of the words are: B, A, S, A, B, B, R, N, B, C.

Answer
BINARY = BRAINY
ABROAD = ABOARD
RASCAL = SCALAR
ALTARS = ASTRAL
BADGER = BARGED
BARKED = BRAKED
MARBLE = RAMBLE
UNABLE = NEBULA
TABLET = BATTLE
CALLER = CELLAR or RECALL

There are some less common anagrams such as:
RASCAL = SACRAL
ALTARS = TARSAL
ALTARS = RATALS
ALTARS = TALARS
BADGER = GARBED
BARKED = DEBARK
MARBLE = BLAMER
MARBLE = AMBLER
MARBLE = LAMBER
UNABLE = UNBALE
TABLET = BATTEL

So you can have an extra half point if you found one of these! There are some even rarer anagrams, but I don't think I'll allow those!

Workings

Hint
The sequence involves doubling in some way.

Answer
75.

Alternately double plus one, double minus one.