Question

Twenty caravans are travelling through the desert one day apart. The first caravan
reached an 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 left . On the third day the third caravan reached the oasis and the
camels drank one quarter of the water left in the pool. On the first day the pool
contained 1050 cubic litres of water. How much water was left after the 20th
caravan passed through.
(Hint: observe the pattern and calculate)

Answer 1

Step-by-step explanation:

let the original amount of water present in oasis be x m².

then,

amount of water drank by first camel =

½x

water left = ½x

then

amount of water drank by second camel = ½•⅓x = 1/6x

water left = ½x – 1/6x = ⅓x

then

amount of water drank by third camel =

¼•⅓x = 1/12x

water left = ⅓x – 1/12x = 1/4x

from here we can see that on n-th day the camel drank 1/(n+1) part of water that was left and amount of water that WAS left is (1/n)x.

SO THE AMOUNT OF WATER THAT IT DRiNK IS [ (1/n) - (1/(n)(n+1)) ] x = x/(n+1)

so,

on 20 th day,

x/21 = 1050/21 = 50 m² is the amount of water left