Twenty caravans are travelling across the desert one day apart. The first caravan reaches the oasis and the camel drank half of the water in the pool. On the second day, the second caravan reaches the oasis and the camel drank one third of the water that was left. On the third day the camel in the third caravan drank one quarter of the water that was left. On the first day the pool contained 1050 sq.metre of water. How much water was left after the twenty caravan passed through.
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Answers
let the total number of water in the pool before any caravan arrives is x
on 1st day : given that the 1st caravan drank half the water
⇒ the 1st caravan drank x/2 water and the remaining water is x/2
on 2nd day: given that the 2nd caravan drank (1/3)rd of the remaining water
⇒ the water remaining after the 2nd caravan drank is : (x/2) - 1/3(x/2)
⇒ x/2(1 - 1/3) = x/2 × 2/3 = x/3
⇒ the water remaining after the 2nd caravan drank is x/3
on the 3rd day : given that the 3rd caravan drank (1/4)th of the remaining water
⇒ the water remaining after the 3rd caravan drank is : (x/3) - 1/4(x/3)
⇒ x/3(1 - 1/4) = x/3 × 3/4 = x/4
the water remaining after the 3rd caravan drank is x/4
with keen observation we can notice that there is a pattern that is:
after the completion of 1st caravan drinking the water remaining is x/2
after the completion of 2nd caravan drinking the water remaining is x/3
after the completion of 3rd caravan drinking the water remaining is x/4
⇒From the above pattern : after the completion of 20th caravan drinking the water we can confidently say that the remaining water in the pool is x/21
Given: total number of water in the pool before any caravan arrives is 1050m³
⇒ x = 1050m³
we know that after the completion of 20th caravan drinking the remaining water in the pool is x/21
⇒ remaining water in the pool is (1050/21)m³ = 50m³
So we conclude that the water remaining in the pool after 20 caravans passed is 50m³