Question

rational numbers Ques;;:::::::: 20 caravans are travelling across a desert apart. The first caravan reach the oasis and camels drank half of the water from the pool. On the second day second caravan reach the oasis and drank one third of water which was left. On the third day the camals in the third caravan reaches the oasis and drank one qauter water which was left. On the first day pool contained 1050msquare 3 of water. how much water left when the 20th caravan passed through

Answer 1

As we can see there is a definite, diminishing pattern here. The total water in the pool is 1050 cubic meters.

The first caravan drinks half of that. That is, the first caravan drinks $\frac{1050}{2}$. Likewise, the second caravan drinks third of the remaining. Thus the second caravan drinks $\frac{\frac{1050}{2}}{3}$. Likewise, we get a sequence, the corresponding series of which will give us the total water that the caravans drank. The series will be as:

$\frac{1050}{2}+\frac{1050}{2\times 3}+\frac{1050}{2\times 3\times 4}+\frac{1050}{2\times 3\times 4\times 5}+...+\frac{1050}{2\times 3\times 4\times...\times 21}$

This can be rewritten as a summation as:

$\sum _{n=1}^{20}\frac{1050}{(n+1)!}$

The above summation comes out to be $\sum _{n=1}^{20}\frac{1050}{(n+1)!}\approx 754.2$

Thus, the amount of water left when the 20th caravan passed through is: $1050-754.2=295.8$ cubic meters