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The following question have three statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. In a cinema hall, the amount collected after selling the tickets was Rs. 37500. Find the cost of a ticket if the cost of every ticket is same. Statement I: If the price of each ticket is increased by Rs. 30, the amount collected will be Rs. 4500 more. Statement II: Ratio of number of tickets and the cost of a ticket is 3 : 5. Statement III: If the number of tickets is decreased by 30 (keeping the cost per ticket constant), the amount collected will be Rs. 7500 less.

The following question have three statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. In a cinema hall, the amount collected after selling the tickets was Rs. 37500. Find the cost of a ticket if the cost of every ticket is same. Statement I: If the price of each ticket is increased by Rs. 30, the amount collected will be Rs. 4500 more. Statement II: Ratio of number of tickets and the cost of a ticket is 3 : 5. Statement III: If the number of tickets is decreased by 30 (keeping the cost per ticket constant), the amount collected will be Rs. 7500 less. Correct Answer Any of the statements alone is sufficient to answer the question.

Suppose the price of a ticket is Rs. x;

⇒ Number of tickets = 37500/x

Statement I: 

(x + 30) × 37500/x = 37500 + 4500

⇒ x = 250

⇒ Price of a ticket = Rs. 250

Statement II:

Ratio of number of tickets and the cost of a ticket is 3 : 5.

Suppose the number of tickets and the cost of a ticket is 3a and 5a respectively;

⇒ 15a2 = 37500

⇒ a2 = 2500

⇒ a = 50

∴ Price of a ticket = Rs. 250

Statement III: 

⇒ x × = 37500 - 7500

⇒ x = 250

∴ Price of a ticket = Rs. 250

∴ Any of the statements alone is sufficient to answer the question.

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