Question

A man is stranded on a desert island. All he has to drink is a $20cc$ bottle of apple-o-juice. To conserve his drink he decides that on the first day he will drink one cc and refill the bottle back up with water. On the ${2^{nd}}$ day he will drink $2cc$ and refill the bottle. On the ${3^{rd}}$ day he will drink $3cc$ and so on… By the time all the apple-of-juice is gone, how much water has he drunk?
$\left( a \right){\text{ 190}}$
$\left( b \right){\text{ 210}}$
$\left( c \right){\text{ 160}}$
$\left( d \right){\text{ None of these}}$

Answer 1

For solving this question we will use the concept of adding $n$ natural numbers. And the formula is given by $\dfrac{{n\left( {n + 1} \right)}}{2}$ and for this, we will find the value of $n$ first by reading the question carefully. By going through all these steps we will get the answer for it.

Formula used:
So the formula for adding the $n$ natural number is given by
$\dfrac{{n\left( {n + 1} \right)}}{2}$
Here, $n$ , will be the natural number.

Complete step-by-step answer:
So in the question, we have a man who drinks $20cc$ a bottle of apple-o-juice. And also it is given that on the first day he will drink one cc and refill the bottle back up with water. On the ${2^{nd}}$ day he will drink $2cc$ and refill the bottle and so on it continues till the last ball which will be ${20^{th}}$ .
So on the ${19^{th}}$ day, he will drink the $19L$ of the drink.
Therefore, by using the formula of adding natural numbers. So here the value of $n$ will be equal to $19L$
Substituting the values, in the formula, we have
$\Rightarrow \dfrac{{19 \times 20}}{2}$
And on solving the multiplication we will get the fraction as
$\Rightarrow \dfrac{{380}}{2}$
And on dividing it, we will get
$\Rightarrow 190$
Hence, he will add $190litres$ of water till all the juice is empty.
Therefore, the option $\left( a \right)$ is correct.

Note: For solving this type of question we just need one thing very seriously. That is to go through the problem once, and then only we can get the ideas and implement them. Also while calculating the value for $n$ , we will always keep it less than one, wherever this type of question arises.