Coded language puzzle!!

Question

Here is a puzzle I can't crack. It goes like this:

In a certain coded language

MANGO=3/5

ORANGE=2/6

APPLE=1/5

Then, POTATO=??

The answer is 5/6. I would like to know to arrive at the answer.

Answer 1

HINT: It appears that the denominator is the number of letters in the word. The numerator also appears to be a count: specifically, it appears to be the number of letters of the word that come from a certain $3$-letter set. That is, there are three letters, $\ell_1,\ell_2$, and $\ell_3$, such that MANGO contains all $3$ of them, ORANGE contains $2$ of them, and APPLE contains just one of them. Once you identity these three letters (which can be arranged to form a common word), see how many of them are in POTATO.

Note that there may be other solutions leading to different answers.

Answer 2

I would claim there is not enough information. It appears we are counting the fraction of letters in the word that come from some set. From the first two, we know that $M$ counts, $E,R$ do not, and we have two out of $A,N,G,O$. The third tells us that one of $A$ or $L$ counts, the other and $P$ do not. So it could be $1,2,$ or $3$

Answer 3

My reasoning would be:

The denominator is the number of letters in the word. The numerator is the longest initial segment that forms an English word.

MANGO - MAN = 3

ORANGE - OR = 2

APPLE - A = 1

Then, POTATO - POT = 3

Answer 3/6