Question

At a party, colas, squash and fruit juice were offered to guests. A fourth of guests drank colas, a third drank squash, two fifth drank fruit juice and just three did not drink anything. How many guests were there in total?

Answer 1

Hint: Let us assume the total number of guests in the party as x. Now we will find the number of guests who drank colas. Also, we will find the number of guests who drank squash. Now we will find the number of guests who drank fruit juice. We know that the total number of guests in the meeting are equal to the sum of the number of guests who drank colas, number of guests drank squash, number of guests drank fruit juice and number of guests did not drink anything. From this we will get the number of persons who did not drink anything in terms of x. In the question, it was given that the number of guests who did not drink anything were three. By this we can get the value of x.

Complete step by step solution:
From the question we were given that at a party, colas, squash and fruit juice were offered to guests. A fourth of guests drank colas, a third drank squash and two fifth drank fruit juice.
Let us assume the total number of guests as x.
Number of guests drank colas \[=\dfrac{x}{4}\]
Number of guests drank squash \[=\dfrac{x}{3}\]
Number of guests drank fruit juice \[=\dfrac{2x}{5}\]
Let us assume number of guests did not drink anything \[=y\]
We know that the total number of guests in the meeting are equal to the sum of the number of guests who drank colas, number of guests drank squash, number of guests drank fruit juice and number of guests did not drink anything.
So, we get
\[\begin{align}
  & \Rightarrow x=\dfrac{x}{4}+\dfrac{x}{3}+\dfrac{2x}{5}+y \\
 & \Rightarrow y=x-\dfrac{x}{4}-\dfrac{x}{3}-\dfrac{2x}{5} \\
 & \Rightarrow y=x-\dfrac{7x}{12}-\dfrac{2x}{5} \\
 & \Rightarrow y=x-\dfrac{59x}{60} \\
\end{align}\]
\[\Rightarrow y=\dfrac{x}{60}.....(1)\]
In the question, we are given that the number of guests who did not drink anything are 3.
So, from equation (1) we get
\[\dfrac{x}{60}=3\]
By using cross multiplication, we get
\[\Rightarrow x=180....(2)\]
So, from equation (2) we can get the number of guests equal to 180.

Note: In solving this problem, students may make silly mistakes which results in wrong answers. While solving, if at any place we did addition instead of subtraction and subtraction in addition may result in the wrong answer. These mistakes seem to be simple but it will change the final answer. So, we must be careful and watchful of these mistakes.