Random Puzzles 

Workings

Hint
How many students study chemistry and physics, but not biology?

Answer
500 students.

Reasoning
The answer is more easily seen if three intersecting circles are drawn, and the numbers inside each section are worked out.

We know that 73 students study all three disciplines, which allows us to work out the numbers.

97 students study chemistry and physics, so 97 – 73 = 24 study just chemistry and physics.
138 students study physics and biology, so 138 – 73 = 65 study just physics and biology.
152 students study chemistry and biology, so 152 – 73 = 79 study just chemistry and biology.

280 students study chemistry, so 280 – 73 – 24 – 79 = 104 study just chemistry.
254 students study physics, so 254 – 73 – 24 – 65 = 92 study just physics.
280 students study biology, 280 – 73 – 65 – 79 = 63 study just biology.

For a total of: 104 + 92 + 63 + 24 + 65 + 79 + 73 = 500 students.

Workings

Hint
A little algebra might help.

Answer
I will be 35 in 14 years.

Reasoning
I am currently 21.

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

   2X = 14
  ———
   3

and

  2X = 42

So

  X = 21

I am currently 21 and my favourite book is currently 14 years old, when it is 28 years old (double its age) I will be 35.

Workings

Hint
Where did Strumpy finish?

Answer
Name     Town        #    Routine
Boo Boo  Shrimpton   2^nd  Flower
Strumpy  Stockville  4^th  Unicycle
Tambo    Budsworth   5^th  Custard Pie
Grego    Whitfield   7^th  Rubber Mallet

The positions that the four clowns could finish are 2^nd, 4^th, 5^th and 7^th. The Budsworth clown finished one place below Strumpy (1) so Strumpy must have been 4^th and the Budsworth clown 5^th. The (male) clown on the unicycle finished two places below Boo Boo (2) so must have been 7^th or 4^th. Since the clown who came 7^th was female, the clown on the unicycle must have been 4^th and is Strumpy and Boo Boo came 2^nd. Tambo (male) is not the clown who came 7^th (3), 2^nd (Boo Boo) or 4^th (Strumpy) so came 5^th with his custard pie act (4) and Grego came 7^th with her rubber mallet so by elimination, Boo Boo's act involved the flower. The Budsworth clown (Tambo) came 5^th, neither Strumpy (1) nor Boo Boo (2) came from Whitfield so the clown from Whitfield was Grego (7^th). The Shrimpton clown was placed higher than the Stockville clown (4) so came 2^nd and the Stockville clown came 4^th.

Workings

Hint
Work out the total number of legs.

Answer
23 children (46 legs).

With 230 ants (1380 legs), 3 puppies (12 legs), and 1 teacher (2 legs).

If we call the number of puppies P, then there were (P + 20) children and 10 x (P + 20) ants, and a single teacher. If we now count the legs, we get:
Puppies:
 P x 4 =  4P

Children:
 (P + 20) x 2 =  2P + 40

Ants:
 10 x (P + 20) x 6 = 60P + 1200

Teacher: 2

A total of 66P + 1242

Giving:

 66P + 1242 = 1440

 66P        = 198

   P        = 3

So there were 3 puppies, hence 23 children.