Question:
Tickets for a concert were sold at Rs. 2, Rs. 4, and Re. 1. Twelve more tickets were sold at Rs. 4 instead of Rs. 2, and twice tickets were sold at Re. 1. If the total amount collected is Rs. 288, then how many tickets of Rs. 2 were sold?
Tickets for a concert were sold at Rs. 2, Rs. 4, and Re. 1. Twelve more tickets were sold at Rs. 4 instead of Rs. 2, and twice tickets were sold at Re. 1. If the total amount collected is Rs. 288, then how many tickets of Rs. 2 were sold?
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In problems involving multiple categories and total amounts, assign variables for each category, set up an equation, and solve for the unknowns.
Updated On: Dec 12, 2025
- 30
- 24
- 25
- 28
- 22
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The Correct Option is A
Solution and Explanation
Step 1: Assign variables.
Let the number of tickets sold at Rs. 2 be \( x \). Then, the number of tickets sold at Rs. 4 will be \( x + 12 \), and the number of tickets sold at Re. 1 will be \( 2x \).
Step 2: Set up the equation based on the total amount collected.
The total amount collected is Rs. 288. The amount collected from each type of ticket is: - From Rs. 2 tickets: \( 2x \) - From Rs. 4 tickets: \( 4(x + 12) \) - From Re. 1 tickets: \( 1(2x) \) Thus, the total amount collected is: \[ 2x + 4(x + 12) + 2x = 288 \] Step 3: Solve the equation.
Simplify the equation: \[ 2x + 4x + 48 + 2x = 288 \] \[ 8x + 48 = 288 \] \[ 8x = 288 - 48 = 240 \] \[ x = \frac{240}{8} = 30 \] Step 4: Conclusion.
Thus, the number of tickets sold at Rs. 2 is 30.
Let the number of tickets sold at Rs. 2 be \( x \). Then, the number of tickets sold at Rs. 4 will be \( x + 12 \), and the number of tickets sold at Re. 1 will be \( 2x \).
Step 2: Set up the equation based on the total amount collected.
The total amount collected is Rs. 288. The amount collected from each type of ticket is: - From Rs. 2 tickets: \( 2x \) - From Rs. 4 tickets: \( 4(x + 12) \) - From Re. 1 tickets: \( 1(2x) \) Thus, the total amount collected is: \[ 2x + 4(x + 12) + 2x = 288 \] Step 3: Solve the equation.
Simplify the equation: \[ 2x + 4x + 48 + 2x = 288 \] \[ 8x + 48 = 288 \] \[ 8x = 288 - 48 = 240 \] \[ x = \frac{240}{8} = 30 \] Step 4: Conclusion.
Thus, the number of tickets sold at Rs. 2 is 30.
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