There is a 15% discount for a conference ticket if it is bought 5 to 29 days in advance. The discount is 30%, if the ticket is bought 30 to 59 days in advance. The discount is 40%, if the ticket is bought 60 to 89 days in advance. Sheela paid Tk 252 for the conference ticket. If she had purchased the ticket one day later, she would have paid Tk 306. How many days in advance did she purchase the ticket?

Explanation: There are three cases when the price of the ticket will increase if it is bought one day later. Case 1 (5 days in advance): \(Tk~252\) is \(15\%\) discount price, and \(Tk~306\) is total price. \(306 \times (1-0.15) \ne 252\). Not 5 days. Case 2 (30 days in advance): \(Tk~252\) is \(30\%\) discount price, and \(Tk~306\) is \(15\%\) discount price. Total price from \(Tk~252\) is \(252 / (1-0.30) = 360\). Total price from \(Tk~306\) is \(306 / (1-0.15) = 360\). Total price is same (\(Tk~360\)). So, the ticket was actually bought 30 days in advance. Case 3 (60 days in advance): No need to check.