By increasing the price of entry ticket to a fair in the ratio 3 : 5, the number of visitors to the fair has decreased in the ratio 7 : 2.…

Let the price of the ticket be y

And the number of visitors be z

Then if price of ticket is increased in ratio 3 : 5 the visitors decreased in ratio 7 : 2

i.e. when ticket price = 3y/8

then number of visitors = 7z/9

So total collection before = (3y/8) × (7z/9) = 7yz/24

Now after increasing price tickets

Ticket price = 5y/8

⇒ Number of visitors = 2z/9

⇒ Total collection after = (5y/8) × (2z/9) = 5yz/36

So, it is clear that the collection after has decreased.

Ratio = (7yz/24) : (5yz/36) = 21 : 10

So the total collection has decreased by the ratio 21 : 10