Question

Some tickets of Rs 200 and some of Rs 100, of a drama in a theatre were sold. The number of tickets of Rs 200 sold was 20 more than the number of tickets of Rs 100. The total amount received by the theatre by sale of tickets was Rs 37000. Find the number of Rs 100 tickets sold.

Answer 1

Hint: Here, we will proceed by assuming x as the number of Rs 100 tickets sold and then we will be multiplying the cost of per ticket with the number of tickets sold of that type and then adding all the amounts obtained by different types of tickets.

Complete step-by-step answer:
Let the number of Rs 100 tickets sold be x.
Given, Number of Rs 200 tickets sold = Number of Rs 100 tickets sold + 20
Number of Rs 200 tickets sold = (x+20)
Since, Amount received by the theatre by sale of Rs 100 tickets = 100$ \times $(Number of Rs 100 tickets sold)
$ \Rightarrow $Amount received by the theatre by sale of Rs 100 tickets$ = 100 \times \left( x \right) = {\text{Rs }}100x$
Similarly, Amount received by the theatre by sale of Rs 200 tickets = 200$ \times $(Number of Rs 200 tickets sold)
Amount received by the theatre by sale of Rs 200 tickets$ = 200 \times \left( {x + 20} \right) = {\text{Rs }}\left( {{\text{2}}00x + 4000} \right)$
It is also given that,
Total amount received by the theatre by sale of tickets = Rs 37000
As we know that the total amount received by the theatre by sale of tickets is equal to the sum of the amount received by the theatre by sale of Rs 100 tickets and the amount received by the theatre by sale of Rs 200 tickets.
i.e., Total amount received by the theatre by sale of tickets = (Amount received by the theatre by sale of Rs 100 tickets) + (Amount received by the theatre by sale of Rs 200 tickets)
$
   \Rightarrow 37000 = 100x + \left( {200x + 4000} \right) \\
   \Rightarrow 37000 = 300x + 4000 \\
   \Rightarrow 300x = 37000 - 4000 \\
   \Rightarrow 300x = 33000 \\
   \Rightarrow x = \dfrac{{33000}}{{300}} \\
   \Rightarrow x = 110 \\
 $
Therefore, the number of Rs 100 tickets sold are 110 tickets.

Note: In this particular problem, we are only asked for the number of Rs 100 tickets sold that’s why we have only calculated the value of x. But in the problem, if it is mentioned that also find the number of Rs 200 tickets sold. Since, the number of Rs 200 tickets sold is equal to (x+20) which will eventually be equal to 130 tickets.