Looking at the questions, only Q2 has an answer that doesn't reference itself directly. For example Q1 asks about c) as an answer, but its answer c) is Q1.
So it's easiest to look at Q2 first.
Q2's answer can't be b) (as this would be an immediate contradiction), so Q4's answer can't be a), so Q2's answer can't be a).
Q2 can therefore be either c) or d).
If Q2's answer was d), then Q1's answer would be a), so Q3's answer would be c), so Q4's answer would be d), so Q1's answer would be b). However this now contradicts itself, so Q2's answer can't be d).
Therefore Q2's answer must be c). Making Q3's answer a), making Q1's answer d), confirming Q2's answer is c). Leaving Q4's answer as b).
These 4-letter words can each have a letter added and then be rearranged to make a new 5-letter word.
HERB + T becomes BERTH
BANG + E becomes BEGAN
KEEN + L becomes KNEEL
SUIT + E becomes SUITE
QUAD + S becomes SQUAD
WHEY + C becomes CHEWY
CELL + O becomes CELLO
TOIL + P becomes PILOT
WILD + E becomes WIELD
Last week I decided to cycle to my Grandmother's house.
On the first day, I cycled half of the distance.
On day 2, I cycled one half of the remaining distance.
On day 3, I cycled three quarters of the remaining distance.
On day 4, I cycled 10 miles.
On day 5 I cycled two thirds of the remaining distance and on the final day I cycled the remaining 5 miles.
On the final day I cycled the remaining 5 miles
On Day 5 I started with 15 miles (as I cycled two thirds, leaving 5 miles).
On Day 4 I started with 25 miles (as I cycled 10 miles).
On Day 3 I started with 100 miles (as I cycled three quarters, leaving 25 miles).
On Day 2 I started with 200 miles (as I cycled half, leaving 100 miles).
On Day 1 I started with 400 miles (as I cycled half, leaving 200 miles).