Random Puzzles 

Workings

Hint
Try working backwards.

Answer
7,340 metres.

Reasoning
Stage 5's clue tells us that 150m was left. So the distance left at the start of Stage 4 must have been:
Dist4 = Dist4 + 75 + 150
        —————
          2

Which simplifies to give Dist4 = 450m.

Stage 3's clue tells us that 450m was one quarter of the remaining distance, so Dist3 = 1,800m.

Stage 2's clue tells us that the distance at the start of Stage 2 was:
Dist2 = Dist2 + 35 + 1800
        —————
          2

Which simplifies to give Dist2 = 3,670m.

Stage 1's clue tells us that 3,670m was half the overall distance, which means the entire ride was 7,340m.

Double-Checking
Starting with 7,340m:
Stage 1: cycled 3,670m, leaving 3,670m

Stage 2: cycled 1,870m, leaving 1,800m

Stage 3: cycled 1,350m, leaving   450m

Stage 4: cycled   300m, leaving   150m

Stage 5: cycled   150m, leaving     0m

Workings

Hint
The word LEMON appears 47 times.

Answer
The word LEMON appears 47 times.

Workings

Hint
A little bit of algebra might help.

Answer
There are four boys and three girls.

If we call the number of boys B, and girls G.

From the first statement (we take one off as Billy is a boy):

              B − 1 = G

and similarly:

        2 x (G − 1) = B

Substitute G from the first equation into the second equation to give:

  2 x ((B − 1) − 1) = B

    2 x (B − 1) − 2 = B

      2 x B − 2 − 2 = B

          2 x B − 4 = B

                  B = 4

which means that B = 4 and hence G = 3.

Workings

Hint
Look for the question.

Answer
N.

Reasoning
Starting with the first letter and taking every other letter gives: TO BE OR NOT TO BE TH

Starting with the second letter and taking every other letter gives: AT IS THE QUESTIO

Combining gives: TO BE OR NOT TO BE THAT IS THE QUESTIO, and the last letter of QUESTION is missing.