Random Puzzles 

Workings

Hint
Find the weight of the bottle first.

Answer
24 ounces.

The bottle weighs 16 ounces.

Reasoning
As a bottle (B) weighs eight ounces plus half a bottle, we can write this as:
   B = 8 + ¹/₂ x B
  ¹/₂ x B = 8
   B = 16

As the bottle weighs 16 ounces, a bottle and a half weighs 16 + 8 = 24 ounces.

Workings

Hint
Look at every third letter.

Answer
The BrainBashers electronic word processor has been playing up.

It is replacing every third letter with an a. What should this paragraph read?

Workings

Hint
Try finding the cube root of 190,747.

Answer
53, 59, and 61.

Reasoning
Start by taking the cube root of 190,747, which is approximately 57.56.

The next highest prime number is 59:

   190,747 ÷ 59 = 3,233

Let's try the next prime number, which is 61:

     3,233 ÷ 61 = 53

53, 59, and 61, are all prime, and are consecutive, so this is the answer.

Double-Checking
   53 x 59 x 61 = 190,747

Workings

Hint
Try working backwards.

Answer
£98.82.

Reasoning
At the end I was left with £32.94, which was half of my remaining money, so before buying the trousers I must have had £65.88.

Again, this was half of my money, so before buying the jacket I must have had £131.76 at the start.

As I now had £32.94 remaining, I must have spent £98.82.

Double-Checking
I started with £131.76, and I spent £65.88 on a new jacket, and then £32.94 on the trousers, a total spend of £98.82.