Question

For a club anniversary dinner, some members and some of their guests attended the dinner. The guests were \[\dfrac{1}{3}\] of the number of members. Each guest paid ₹ 400 and each member paid ₹ 300. The total sum collected for the event was ₹ 1,04,000. Find the number of members who attended the event.

Answer 1

Hint: Here, we need to find the number of members who attended the event. We will assume the number of members who attended the event to be \[x\]. Using the given information we will form an equation in terms of \[x\]. Then, we will solve the equation to find the value of \[x\], and hence, the number of members who attended the event.

Complete step-by-step answer:
Let the number of members who attended the event be \[x\].
We know that the number of guests who attended the event is \[\dfrac{1}{3}\] of the number of members.
Therefore, we get
Number of guests who attended the event \[ = \dfrac{1}{3}\]
or \[x = \dfrac{x}{3}\]
Now, we will find the total sum collected from the members and the total sum collected from the guests.
The total sum collected from the members will be the product of the amount paid by 1 member and the number of members who attended the event.
Therefore, we get
Total sum collected from the members \[ = 300 \times x = 300x\] rupees
Next, the total sum collected from the guests will be the product of the amount paid by 1 guest, and the number of guests who attended the event.
Therefore, we get
Total sum collected from the guests \[ = 400 \times \dfrac{x}{3} = \dfrac{{400x}}{3}\] rupees
Now, the total sum collected for the event will be the sum of the total amount collected from the members and the total amount collected from the guests.
Therefore, we get
Total sum collected for the event \[ = 300x + \dfrac{{400x}}{3}\]
It is given that the total sum collected for the event was ₹ 1,04,000.
Therefore, we get the equation
 \[ \Rightarrow 300 x + \dfrac{{400x}}{3} = 104000\]
We will solve this equation to find the value of \[x\].
Taking the L.C.M. of the terms, we get
\[ \Rightarrow \dfrac{{900x + 400x}}{3} = 104000\]
Adding the like terms in the numerator, we get
\[ \Rightarrow \dfrac{{1300x}}{3} = 104000\]
Multiplying both sides 3, we get
\[\begin{array}{l} \Rightarrow \dfrac{{1300x}}{3} \times 3 = 104000 \times 3\\ \Rightarrow 1300x = 312000\end{array}\]
Dividing both sides by 1300, we get
\[\begin{array}{l} \Rightarrow \dfrac{{1300x}}{{1300}} = \dfrac{{312000}}{{1300}}\\ \Rightarrow x = 240\end{array}\]
\[\therefore\] We get the number of members who attended the event as 240.

Note: You should read the question carefully. The first line of the question states ‘members’ before ‘guests’. However, it states the amount paid by a guest before the amount paid by a member. A common mistake is to read that ͅ₹ 400 is written before ₹ 300, and therefore use it as the amount paid by each member. That is incorrect.