Random Puzzles 

Workings

Hint
The first word begins with T.

Answer
Too many cooks spoil the broth.

Reasoning
The saying has been broken down into blocks of 4, the last block has been filled with dummy letters. Each block has then been reversed.

Double-Checking
Start with:
   TOO MANY COOKS SPOIL THE BROTH

Group together:
   TOOMANYCOOKSSPOILTHEBROTH

Split into groups of 4 letters:
   TOOM ANYC OOKS SPOI LTHE BROT H

Add 3 random characters:
   TOOM ANYC OOKS SPOI LTHE BROT HBCY

Reverse each group of 4 letters:
   MOOT CYNA SKOO IOPS EHTL TORB YCBH

Workings

Hint
Try a random number of over 50s to see what happens.

Answer
20,064 apples.

Reasoning
It doesn't matter how old the people are.

As only ³/₄ of the over 50s claimed 16 apples, this averages out to 12 apples each.

Similarly, only ¹/₈ of the under 50s claimed 96 apples, this again averages out to be 12 apples each.

Therefore, the total number of apples was 1,672 x 12 = 20,064.

Workings

Hint
Look at the edges first.

Answer
 

Workings

Hint
It doesn't actually matter how many men or women there were.

Answer
17,760 dollars.

If there were M men, then there were (3552 − M) women.

So one ninth of the men each received 45 dollars and one twelve of the women each received 60 dollars. So the total received was:
= 45 x 1 x M  +  60 x  1 x (3552 − M)
       —              ——
       9              12

Simplify the two fractions by dividing the 45 by 9, and the 60 by 12 respectively.

= 5 x M + 5 x (3552 − M)

= 5M + 17760 − 5M

= 17760