The bar account

The bar account

Antonio, Begoña, Carlos and Diana have had a snack at the bar. When paying, they do it equally. Once the account is paid, they prove that although everyone has paid the same, Antonio has put 10% of the money he had, Begoña 20%, Carlos 30% and Diana 40%.

If we know that at the beginning they all had a whole number of euros (without cents),

How much money did each initially have at least?


If we identify each person with the initial of his name Antonio (to), Begoña (b), Charles (c) and Diana (d),
with the data they give us, we have to 10% to = 20% b = 30% c = 40% d.
Or what would be the same, 0'1to = 0'2b = 0'3c = 0'4d.
If we put them in function of to, we have to to = 2b = 3c = 4d.

As they tell us that at the beginning all of them had an integer number of euros, we calculate the least common multiple of the 4 numbers (1,2,3,4), which is 12. And therefore, we know that to, has 12 euros, which b, which has half, has 6 euros, c, the third part, 4 euros, and d, the fourth part, 3 euros. So everyone paid 1.2 euros.