Random Puzzles 

Workings

Hint
Adding 900,000 to the numbner is the same as placing a 9 at the beginning.

Answer
23,076.

Reasoning
Placing the 9 at the beginning is equivalent to adding 900,000 (for example, 12,345 + 900,000 becomes 912,345).

Placing the 9 at the end is equivalent to multiplying by 10 and adding 9 (for example, 12,345 x 10 + 9 becomes 123,459).

Let's call the unknown number k, and we know that one of these numbers is 4 times the other, so:

 k + 900,000 = 4 x (10k + 9)

 k + 900,000 = 40k + 36

900,000 − 36 = 40k − k

     899,964 = 39k

899,964 ÷ 39 = k

Therefore, k = 23,076.

Double-Checking
923,076 = 4 x 230,769.

Workings

Hint
There are at least two different answers.

Answer
BRAKING becomes BREAKING

or

BROWS becomes BROWSE

Workings

Hint
One inch = 25.4mm.

Answer
Millimetres in a mile.

Reasoning
One inch = 25.4mm.

So:

1 mile = 1760 yards = 1760 x 3 feet = 1760 x 3 x 12 inches = 1760 x 3 x 12 x 25.4 millimetres = 1,609,344mm in 1 mile.

And:

2 kilometres = 2000 metres = 2000 x 100 centimetre = 2000 x 100 x 10 millimetres = 2000 x 100 x 10 ÷ 25.4 inches = 2000 x 100 x 10 ÷ 25.4 x 16 = sixteenths of an inch ≈ 1,259,843 sixteenths of an inch in 2 kilometres.

Workings

Hint
The answer is in the question.

Answer
Wrong.