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In a cinema hall, 300 tickets were sold. The total sale of tickets was Rs. 1250. If the tickets were of two denominations of Rs. 2.50 and Rs. 5.00, how many of each was sold?

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Last updated date: 22nd Mar 2024
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MVSAT 2024
Answer
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Hint: Try to find a relationship with the number of tickets sold and the price of per ticket.

Complete step by step answer:
Given: Total number of tickets sold which are $300$ and the total sale of tickets is Rs. $1250$ in which denomination of Rs.$2.50$ and Rs. $5.00$ are there.
As tickets of only two denominations were sold which are Rs. 2.50 and Rs. 5.00, it means only two types of tickets are sold.
As the number of tickets sold for both the denominations are unknown, So let’s assume the number of tickets of the valuation of Rs.2.50 be $x$and the number of tickets sold for denomination of Rs.5.00 be$y$. Then total revenue from tickets of denomination of Rs.2.50 will be $\left( {2.50} \right)x$and total revenue from tickets of denomination of Rs.5.00 will be$\left( {5.00} \right)y$.
Therefore, $x + y = 300$,$ \to $ (Equation 1)
And $\left( {2.50} \right)x + \left( {5.00} \right)y = 1250$.$ \to $ (Equation 2)
Now, we will Solve the second equation, take out common values from the equation
$2.50\left( {x + 2y} \right) = 1250$,
Now, divide both sides by 2.50, then:-
$
  \dfrac{{2.50\left( {x + 2y} \right)}}{{2.50}} = \dfrac{{1250}}{{2.5}} \\
   = x + 2y \\
   = 500 \\
$ (Equation 3)
Now, we have a new equation named equation (3)
Now, we will Subtract this equation (3) form (1), which will be:
$x - x + 2y - y = 500 - 300$
Now, we found out the value of $y$ by solving the upper equation which is$y = 200$,
Now, substitute the value of $y$ in equation (1) to find out the value of $x$.
$
  x + y = 300 \\
  x + 200 = 300 \\
  x = 300 - 200 \\
  x = 100 \\
$
So, we have found the number of tickets which were sold of denomination of Rs. 2.50 is 100 and of Rs. 5.00 is 200.

Note: let the number of tickets of denomination Rs.$2.50$ be $x$ and the number of tickets of denominations Rs.$5.00$ be $y$ then make the equation using these two variables according to the value given in the question.