Question

Twenty caravans are traveling across the desert one day apart. The first caravan reached the oasis, and the camels drank half of the water in the pool. On the second day, the second caravan reached the oasis, and the camels drank one-third of the water that was left. On the third day, the camels in the third caravan drank one-quarter of the water that was left. On the first day, the pool contained 1050 m³ of water. How much water was left after the 20th caravan passed through?​

1. ThanhThu
The water that was left after the 20th caravan passed through the pool is 50 m³. Using fractions, the required value is obtained.

### What are fractions?

A fraction is a rational number that has the required part and whole part of an object.

### Calculation:

It is given that,
The total volume of the water in the pool is W = 1050 m³
Twenty caravans are traveling across the desert one day apart.
1) On the first day, the camel consumed half of the water in the pool.
Then we can write, water consumed by the camels on the first day = 1/2 × W
So, the remaining water left in the pool = W – W/2 = W/2 …(i)
2) On the second day, the camel consumed one-third of the water in the pool.
Then, water consumed by the camels on the second day = 1/3 × W/2 = W/6
So, the remaining water left in the pool = W/2 – W/6 = 4W/12 = W/3 …(ii)
3) On the third day, the camel consumed one-quarter of the water in the pool.
Then, water consumed by the camels on the third day = 1/4 × W/3 = W/12
So, the remaining water left in the pool = W/3 – W/12 = 3W/12 = W/4 …(iii)
From (i), (ii), and (iii) we can observe that the denominator of the remaining water volume is increased by 1 every next day.
I.e., the general form we can write here is W/(n + 1)
Where W – the volume of the water; n – the number of days it reaches the pool.
Thus, on the 20th day, the camels will consumed the remaining water. I.e.,
The remaining water left in the pool = W/(20 + 1) = W/21
But we have W = 1050 m³
On substituting,
The remaining water left in the pool after the 20th caravan passed through = 1050/21 = 50 m³