Random Puzzles 

Workings

Hint
Remember that you have the same number of each coin.

Answer
134 of each coin.

Reasoning
We have equal numbers of 2p, 5p, 10p, and 20p.

And 2p + 5p + 10p + 20p = 37p.

There are 134 lots of 37p in £49.58.

Double-Checking
134 x 37 = 4958.

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
Look at the vowels (AEIOU).

Answer
7.00pm.

Each vowel (AEIOU) of the country is worth 2 hours, and each consonant is worth 3 hours.

The time shown is the number of hours past midnight of the return trip.

Workings

Answer
1680.

This is n to the power of 5, starting with 2^5 = 32, with the last digit missing, 7^5 = 16807.