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.