Question

Some tickets of Rs. $ 200 $ and some of Rs. $ 100 $ , of a drama in a theatre were sold. The number of tickets 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: We will take $ x $ as the numbers of tickets costing Rs. 200 And let y as tickets costing Rs. 100. After that we will form the equations for both the statements and we will try to solve the equation as we have two unknowns and two equations, we can solve this and find the appropriate value of x and y respectively.

Complete step-by-step answer:
 Here we have two types of tickets
Cost of first type of tickets is Rs. 200
Cost of second type of tickets is Rs. 100
Let $ x $ be no. of tickets that were sold each costing Rs. 200.
Cost of $ x $ tickets will be $ 200x $
Let $ y $ be the no. of tickets sold each cost Rs. 100.
Cost of $ y $ tickets will be $ 100y $
As given in the question the total amount received at the theatre by sale of tickets $ x $ and $ y $ was Rs 37000.
Hence from above statement we got the equation as
 $ 200x + 100y = 37000 $ --(1)
Here we are given that the number of tickets of Rs. 200 sold were 20 more than the number of tickets of Rs. 100.
 $ x = y + 20 $ --(2)
Now that we have two equations and two unknown, we can easily find out the value of both the unknowns.
From the above equation (2) we have the x=y+20 so we will put this value of x in the equation (1)
Hence we get,
 $ 200(y + 20) + 100y = 37000 $
 $ \Rightarrow 200y + 4000 + 100y = 37000 $
 $ \Rightarrow 300y = 33000 $
 $ \Rightarrow y = 110 $
So now we have $ y = 110 $
So we have 110 tickets costing Rs. 100
Let’s find the number of tickets costing Rs. 200
By putting the value $ y = 110 $ in equation (2)
We have
 $ x = 110 + 20 = 130 $
Hence, we got that the number of Rs. 100 tickets sold is 110
The number of Rs. 200 tickets sold is 130 respectively.
So, the correct answer is “130”.

Note: While solving two linear equations involving two variables there are various ways to find the solution, but always use the elementary method of putting value from one equation to another as it is convenient and there is no worry about formulas.