Question

For a club anniversary dinner, some members and some of their guests attended the dinner. The guests were `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

Let the number of members be x,

Then, the number of guests is: `1/3x`

Calculating total collection according to the conditions:

Each member paid ₹300 = contribution from members = 300x.

Each guest paid ₹400 = contribution from guests = `400(1/3x) = 400(x/3) = (400x)/3`

So, the total amount collected:

`300x + (400x)/3 = 1,04,000`

Multiplying the equation by 3:

`3(300x) + 3((400x)/3) = 3(1,04,000)`

900x + 400x = 3,12,000

1300x = 3,12,000

x = `(3,12,000)/1300`

∴ x = 240

Hence, the Number of members who attended the event was 240 people,

And the number of guests is `1/3 xx 240 = 80`,

So, the total attendees were 320 people.