Question

$\bigstar$ Start with a full cup of black coffee (no milk) and drink one-third of it.

$\bigstar$ Now pour into the cup an amount of milk equal to the coffee you have just drunk, and stir well.

$\bigstar$ Now drink a further half of the resultant mixture.

$\bigstar$ Now pour into the cup a further amount of milk equal to the mixture you have just drunk and stir well again.

$\bigstar$ Now drink one-sixth of the resultant mixture.

$\bigstar$ Now pour into the cup a further amount of milk equal to the mixture you have just drunk, stir well, and finally, drink the whole cup of liquid.

Have you drunk more milk or more coffee in total?

Answer 1

We have with us, a full cup of black coffee.

Drinking one-third of it, there's two-third of the coffee left.

We've to now pour into it a cup of milk equivalent to the amount of coffee that was drunk [one-third].

If you observe, the amount of coffee becomes the same.

$\sf \Bigg[\dfrac{1}{3}\ +\ \dfrac{2}{3}\ =\ 1\Bigg]$

Now, we're to drink half of the coffee. Again, what remains is another half.

We've to add the same amount of milk as the coffee we drank. Again, the amount of coffee becomes the same.

$\sf \Bigg[\dfrac{1}{2}\ +\ \dfrac{1}{2}\ =\ 1\Bigg]$

Now, we're to drink one-sixth of the coffee. We're left with five-sixth of the mixture.

Again, we're to add an amount of milk [one-sixth] that is the same as the amount of coffee we drank. The resultant amount becomes the same again.

$\sf \Bigg[\dfrac{1}{6}\ +\ \dfrac{5}{6}\ =\ 1\Bigg]$

Therefore, the amount of coffee is the same in each case.

Let's observe the amount of milk that was to be added in each case.

$\sf \dfrac{1}{3},\ \dfrac{1}{2}\ and\ \dfrac{1}{6}.$

On adding these fractions,

$\sf \dfrac{1}{3}\ +\ \dfrac{1}{2}\ +\ \dfrac{1}{6}\ \implies\ \dfrac{2}{6}\ +\ \dfrac{3}{6}\ +\ \dfrac{1}{6}\ =\ 1$

We see that the amount of coffee and milk drunk is the same [one cup].

Therefore, one cup of milk and one cup of coffee was drunk.