Random Puzzles 

Workings

Hint
How many large pipes are required to drain the reservoir in 24 hours?

Answer
21 hours and 36 minutes.

Reasoning
Looking at the first clue:
   in 12 hours, 6 large pipes can drain 1 reservoir
   in 24 hours, 6 large pipes can drain 2 reservoirs
   (*) in 24 hours, 3 large pipes can drain 1 reservoir

Looking at the second clue:
   in 8 hours, 3 large + 9 small pipes can drain 1 reservoir
   in 24 hours, 3 large + 9 small pipes can drain 3 reservoirs

But, by (*), we know that in those 24 hours, 3 large pipes can drain 1 of those reservoirs.

Therefore, the other 2 reservoirs can be drained by the small pipes on their own:
   in 24 hours, 9 small pipes can drain 2 reservoirs
   in 24 hours, 1 small pipe can drain ²/₉ reservoirs
multiply the hours by 9:
   in 216 hours, 1 small pipe can drain 2 reservoirs
   in 216 hours, 5 small pipes can drain 10 reservoirs
divide the hours by 10:
   in 21.6 hours, 5 small pipes can drain 1 reservoir

21.6 hours = 21 hours and 36 minutes.

Workings

Hint
Start by counting the letters you're already given.

Answers
This sentence contains one X. Slightly trickier, this sentence contains four R's. Even trickier, this sentence contains precisely ten E's. This sentence has exactly thirty-nine letters. This sentence, hopefully, contains seventy-five letters, one hyphen, five commas, and four Y's. To finish, if this sentence had a T removed, it would contain sixty-two letters!

Workings

Hint
A little bit of algebra might help.

Answers
Drew is 7 years old. Glen is 4 years old.
Answer #1
The first question involves Drew (D) and Alex (A).

Drew is currently one fifth of Alex's age, so:

(1)      A = D x 5

In 21 years, Alex will be twice their age, so:

(2) A + 21 = (D + 21) x 2

Using (1) in (2) gives:

  A + 21 = (D + 21) x 2

 5D + 21 = (D + 21) x 2

 5D + 21 = 2D + 42

      3D = 21

       D = 7

So Drew is 7 (and Alex is 35).

Answer #2
The second question involves Glen (G) and Billie (B).

Billie is exactly seven times the age of Glen:

(3)     B = G x 7

In 8 years, Billie will be three times the age of Glen, so:

(4) B + 8 = (G + 8) x 3

Using (3) in (4) gives:

  B + 8 = (G + 8) x 3

 7G + 8 = (G + 8) x 3

 7G + 8 = 3G + 24

     4G = 16

      G = 4

So Glen is 4 (and Billie is 28).

Workings

Hint
Start with the possible answers where the first digit is a prime number, and then look at the third digit.

Answer
23,475.

Reasoning
By (1), the first digit is prime:
   2----
   3----
   5----
   7----

By (3), the third digit is twice the first digit, so we can eliminate 5---- and 7----:
   2-4--
   3-6--

By (4), the fourth digit is the third digit plus three:
   2-47-
   3-69-

By (5) the fifth digit is the difference between the first digit and the fourth digit:
   2-475
   3-696

We know from the introduction that no digit is repeated, so we can eliminate 3-696. And, by (2) the second digit is the fifth digit minus the first digit:
   23475