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. In what ratio has the total collection increased or decreased?
1). Increased in the ratio 10 : 21
2). Increased in the ratio 6 : 35
3). Decreased in the ratio 21 : 10
4). Decreased in the ratio 35 : 6
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