Puzzle | Missing One Rupee

Question

I came across the following riddle.

A group of $30$ Indian merchants go to a hotel and stay there for a night. The hotel owner provides for their lunch and breakfast. He serves dinner at the rate of $2$ plates/$\large{₹}$ and breakfast at the rate $3$ plates/$\large{₹}$. When the merchants check out in the morning they are given the bill of $\large{₹}25$ for their food. As per the owner $30$ dinners at the rate of $2$ plates/$\large{₹}$ equals to $\large{₹}15$, and $30$ breakfast at the rate of $3$ plates/$\large{₹}$ equals to $\large{₹}10$, and hence $\large{₹}25$$(10+15)$.
However the merchants give the owner $\large{₹}$$24$ claiming that dinner and breakfast together costed $5$ plates for $\large{₹}$$2$. Therefore, $60$ plates ($30$ of night and $30$ of morning) costs $\frac{2}{5}\times 60 = \large{₹}$ $24$.

Whom do you favor, merchants or the owner, and why?

I am unable to decide who is correct as mathematically they both appear correct to me. Is there a way to find out as to which method is wrong and which is correct one?

Answer 1

The financier in me says that 3 breakfasts at for 1 rupee at 67 rupee / dollar, this hotelier cannot afford to give away food so cheaply. And these merchants should just pay the additional rupee.

Nonetheless... A plate of breakfast is not a plate of lunch. When the merchants say say "5 plates for 2 rupees." That is 2 lunches and 3 breakfasts. Yet, they are not buying 3 breakfasts for every 2 lunches, they are buying an equal number of each, and the lunches cost more.

Answer 2

The merchants divided 60 plates by 5. They cannot do this, as the 60 has 30 lunch and 30 breakfast while the 5 has 3 plates of breakfast and 2 plates of dinner.

If the merchants would be correct, 60 divided by these 5 gives 12. Hence there are 12 of such combinations (3 breakfast and 2 lunch) which means that the total number of breakfast should be 12*3=36 and total number of lunch should be 12*2=24. But that is not the case hence the merchants are incorrect.

Answer 3

Clearly owners are right.

To observe it more clearly ,, Let's make a group of 6 peoples,,(because 6 is fit in 2 plates at 1 rupee, 3 plates at 1 rupee and 30 peoples)

Then the group will have to pay for 6 breakfasts=3 rupees & 6 dinners=2 rupees

Total=5 rupees

We can make 5 such groups as 6$\times 5$=30

Hence total cost=25 rupees

Merchants will be merchants

By the way ,, we have proved owners are right...