Basic arithmetic - trick question.

Question

I have the following question:

A baker filled a measuring cup with $3/4$ cup of water. He poured $1/2$ of the water into the batter, and then spilled $1/8$ of the water on the floor.

How much water will the baker need to add to what is left in the cup to have 50% more than what he started with?

Now, these are the possible answers given by the question:

• $1/8$ cup.
• $3/8$ cup.
• $1/4$ cup.
• $1/2$ cup.
• $7/8$ cup.

Here's what I did:

We start with $$3/4 \rightarrow 6/8,$$ after pouring the water into the batter $$6/8 - 1/2 \implies 6/8 - 4/8 = 2/8$$ and after spilling the water $$2/8 - 1/8 = 1/8.$$

Now, to find how much we need to add, we add $50\%$ of $3/4$ to the original $3/4$, that is $$(1/2)(3/4) + 3/4 = 3/8 + 6/8 = 9/8.$$

So the total amount of water we need to add is $$9/8 - 1/8 = 8/8.$$ But as you can see this is not one of the possible options.

I don't know if I'm doing something wrong or if the answers are incorrect, I suspect that I'm reading something wrong and there's something I'm just not seeing. I ask for your help with this. Thanks in advance.

Answer 1

You may be reading the question wrong. Try to solve it again using a different wording, so instead of subtracting $\frac{1}{2}$ cup of the water try subtracting half of the total amount of water, and try the same with the 1/8.

Answer 2

Briefly: this question, as presented, is poorly worded.

Less Briefly: you subtracted $\frac12$, but you should have multiplied by $1-\frac12$ (that is, by $\frac12$).

In Detail: the baker poured half "of the water". In ordinary English, we would mean that to mean 'half of the water he had in the measuring cup', not '$\frac12$ a cup of water'. If you proceed from here you get the answer $\frac78$, which is presumably what was intended.

However, the question then goes on to say that he spilled $\frac18$ "of the water" on the floor. Following the logic from before, we would expect this to mean 'an eighth of the water he had in the measuring cup', although this phrase is now itself ambiguous (since it could he 'an eighth of the original amount' or 'an eighth after pouring half'). Neither interpretation gets you an answer on the list, unfortunately.