Random Puzzles 

Workings

Hint
The 4^th word begins with the letter F.

Answers
cl--h = cloth (OT) co--h = cough (UG) di-r- = diary (AY) -rea- = freak (FK) in-e- = index (DX) -ok-r = joker (JE) -a-or = manor (MN) -ua-l = quail (QI) re-e- = rebel (BL) -to-e = stove (SV) s-am- = swamp (WP) ya--t = yacht (CH) -eb-a = zebra (ZR)
This puzzle isn't guaranteed to have a unique answer, can you find another?

Workings

Hint
As we don't know how of the people were library members, you can try a random number and see what happens.

Answer
4,200 books.

Reasoning
It doesn't matter how many library members there were, as ¹/₂ of them accepted the books, and each accepted 6 books, which is 3 books per member on average.

Similarly, it doesn't matter how many non-members there were as ³/₄ of them accepted the books, and each accepted 4 books, which is again 3 books per non-member on average.

Double-Checking
Both the members and non-members accepted, on average, 3 books each.

And 1400 x 3 = 4200.

Workings

Hint
How many minutes are between the times?

Answer
50 minutes.

Reasoning
If we call the number of unknown minutes T.

Between four o'clock and eight o'clock, there are 240 minutes.

There is some point between these two times, before which we have 3 lots of T, and after which we have one lot of T plus 40 minutes.

Therefore, in the 240 minutes, there are 4 lots of T plus 40 minutes.

   240 = 4 x T + 40.

Therefore, T = 50 minutes.

Workings

Hint
This puzzle is perhaps easier than it first appears.

Answer
15.

Using normal mathematics!

⁵/₁₅ of 45 = ¹/₃ of 45 = 15.