Question

In a hotel, there are dishonest waiters. one of them takes out one third of the milk from a container full of milk and replaces it with equal quantity of water. a second waiter again takes out one third of the mixture and replaces it with equal quantity of water. the process is repeated by 4 waiters resulting in only 16 litres of milk being left in the container. what is the capacity of the container? (1) 81 litres (2) 72 litres (3) 54 litres (4) 66 litr

Answer 1

Let the amount of milk initially be x.

When the first person takes 1/3 of x the remaining amount is 2/3x

When the second person takes a 1/3 of what remains the remaining amount is :

2/3x - (1/3 × 2/3x) = 2/3x - 2/9x = 4/9x

When the third person takes 1/3 of what is remaining, the remaining amount is :

4/9x - (1/3 × 4/9x) = 4/9x - 4/27x = 8/27x

When the fourth person takes 1/3 the remaining amount is :

8/27x - (1/3 × 8/27x) = 8/27x - 8/81x = 16/81x

This is equal to 16 litres.

Equating the two :

16/81x = 16

x = 16 × 81/16 = 81

The capacity of the container is 81 litres.