QUESTION

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

Hint: Assume number of tickets of 200 sold be x and number of tickets of 100 sold be y. So, the cost of x ticket will be $200x$ and the cost of y tickets will be $100y$ and therefore the sum of cost of x tickets and y tickets will be equal to 37000.

Let the total number of tickets of 200 sold be x,
Therefore, the cost of x tickets $= 200x$.
Let the total number of tickets of 100 sold be y,
Therefore, cost of y tickets $= 100y$
Since we are given that the number of tickets of 200 sold was 20 more than the number of tickets of 100 sold, we get,
x = y +20 $\ldots ..\left( 1 \right)$
The total amount received by the drama theatre by sale of tickets ‘x’ and ‘y’ is 37000.
$\Rightarrow 200x + 100y = 37000$ $\ldots ..\left( 2 \right)$
Now substituting the value of ‘x’ from equation (1) in equation (2), we get,

$\Rightarrow 200(y + 20) + 100y = 37000 \\ \Rightarrow 200y + 4000 + 100y = 37000 \\ \Rightarrow 300y + 4000 = 37000 \\ \Rightarrow 300y = 37000 - 4000 \\ \Rightarrow 300y = 33000 \\ \Rightarrow y = \dfrac{{33000}}{{300}} \\ \Rightarrow y = 110 \\$

To find value of x put value of ‘y’ in equation (1), we get,
$\Rightarrow x{\text{ }} = y + 20 \\ \Rightarrow x = 110 + 20 \\ \Rightarrow x = 130 \\$
Thus, the number of 100 tickets sold = 110.

Note: In solving above question there is very little chance of error. In the above solution we can replace x and y variables as x and x + 20 as mentioned in question that the number of tickets of 200 sold was 20 more than the number of tickets of 100. In the above solution in place of substituting ‘x’ we can substitute ‘y’ by editing equation (1).