The entrance ticket at the City Pride theatre in Pune is worth Rs. 250. When the price of the ticket was lowered, the sale of tickets increased by 50% while the collections recorded a decrease of 17.5%. Find the deduction in the ticket price.

To answer this item, we let x be the price of each of the ticket and y be the number of sales of the ticket.

Initially, x is equal to Rs. 250. Let P be the collection,

xy = P

250y = P

After the ticket price was lowered, the number of sales becomes 1.5y and the total collection was lowered by 17.5% and becomes 0.825P

x₂y₂ = 0.825P

y₂ = 1.5y

x₂ (1.5y) = 0.825P

x₂ = 0.55x

x₂ = (0.55) (250) = 137.5

The new price is now Rs 137.5 which is Rs 112.5 lower than the original price.