Jeeves prepares a hangover cure using four identical cocktail shakers.

F, in your solution, denotes the capacity of one full shaker. In this case, it should be:

F/2 + 4F/5 + F/K = 31/80*4*F.

Solving the above will give k = 4 (F gets reduced).

I don't understand. Why are we multiplying by 1/4?

Lets consider that each shaker is of L ml.
so we have 4, L ml shakers.

If each of them was full, then we would have 4L ml of content in total.

Case 1 : now as per the question it is stated that :
shaker 1 = 1/2 L
shaker 2 = 4/5 L
shaker 3 = 1/k L
shaker 4 = 0 L

Case 2 : mind you, that after the redistribution of content each shaker is 31/80 full meaning :
shaker 1 = 31/80 L
shaker 2 = 31/80 L
shaker 3 = 31/80 L
shaker 4 = 31/80 L
or simple we could say that 4L was the total capacity and 31/80 of 4L will be quantity post redistribution.

Now the total content is same (in terms of ml) in case 1 and case 2, hence :
1/2 L + 4/5 L + 1/k L = 31/80 * 4L
-> solving this we get 1/k = 1/4, hence k = 4.

A. 2
B. 3
C. 4
D. 5
E. 6

Official Solution:


Jeeves prepares a hangover cure using four identical cocktail shakers. The first shaker is \(\frac{1}{2}\) full, the second shaker is \(\frac{4}{5}\) full, the third shaker is \(\frac{1}{k}\) full and the last one is empty. After Jeeves redistributed all the content of the shakers equally into the four shakers, each shaker became \(\frac{31}{80}\) full. What is the value of \(k\)?


A. \(2\)
B. \(3\)
C. \(4\)
D. \(5\)
E. \(6\)


Let's denote the capacity of each shaker by \(x\).

Then, the amount of liquid in the first shaker is \(\frac{1}{2}*x\), the amount of liquid in the second shaker is \(\frac{4}{5}*x\), the amount of liquid in the third shaker is \(\frac{1}{k}*x\), and the amount of liquid in the fourth shaker is 0.

After redistributing the liquid equally among the four shakers, each shaker will contain \(\frac{1}{4}^{th}\) of the total amount of liquid, which is given to be \(\frac{31}{80}*x\), so we have:


Answer: C

The contents of the 3 shakers divided by 4 will fill 31/80 of each of them and they're identical.

[1/2 + 4/5 + 1/K]/4 = 31/80

[1/8 + 4/20 + 1/4K] = 31/80

[1/8 + 1/5 + 1/4K] = 31/80

You multiply both sides with 80

80/8 + 80/5 + 80/4K = 31

10 + 16 + 20/K = 31

20/K = 31 - 26 = 5

5K = 20

K = 20/5 = 4 = Answer C.