Random Puzzles 

Workings

Hint
The first letter can only be B.

Answer
A badger.

Reasoning
My first is in bridge, but not in ridge = B

My second is in awake, and in mistake = A K E

My third is in danger, but not in ranger = D

My fourth is in strange, and in orange = R A N G E

My fifth is in spline, and in nine = I N E

My last is in river, and in diver = R I V E

Workings

Hint
The 8-letter word begins with the letter G.

Answer
Generous.
lend + ge = le + ge + nd = legend

liar + ne = li + ne + ar = linear

pale + ro = pa + ro + le = parole

coin + us = co + us + in = cousin

Workings

Hint
Cockroaches have 6 feet, mice have 4, and birds have 2. They each have one head.

Answer
35 birds, 5 mice, and 10 cockroaches.

Reasoning
Cockroaches have 6 feet, mice have 4, and birds have 2. They each have one head.

We can write down expressions for the heads and the feet, calling birds B, mice M, and cockroaches C.

Counting the heads:
(1)    B +  M +  C =  50

Counting the feet:
(2)   2B + 4M + 6C = 150

We are told that for every mouse there are two cockroaches so, C = 2M. Update (1) and (2) to give:
(3)    B +  3M =  50
(4)   2B + 16M = 150

If we double (3) we get:
(5)   2B +  6M = 100

We can now do (4) – (5) to give:
 10M = 50
   M = 5

So, we have 5 mice (and 10 cockroaches).

We can use M = 5 in (3) to give:
 B + 3 x 5 = 50
    B + 15 = 50
         B = 35

So, C = 10, M = 5 and B = 35.

Double-Checking
10 cockroaches have 10 heads and 60 feet.
5 mice have 5 heads and 20 feet.
35 birds have 35 heads and 70 feet.

The total number of heads = 10 + 5 + 35 = 50.

The total number of feet = 60 + 20 + 70 = 150.

Workings

Hint
How many chocolates can they eat in one hour?

Answer
2 hours.

Reasoning
In one hour, Alex eats 27 chocolates, Billie eats 12, and Charlie eats 21.

A total of 60 chocolates.

Therefore, 120 chocolates would take 2 hours.