Question

180 tickets of a drama were sold. If the rate of the tickets were rupees 250 and rupees 350 per ticket and the total collection is rupees 49000.how many number of ticket were sold having rate rupees 300?

Answer 1

140 tickets were sold at the rate of Rs.250 and 40 tickets at Rs.350.

Also ,If the rate of the ticket  is Rs.300 ,163 tickets were sold for a collection of Rs.49000.

Given:

No:of Tickets sold = 180 .

Total collection for  the tickets =  Rs.49000.

To Find:

The No: of Tickets sold at Rs.250,Rs.350 and Rs.300.

Solution:

Let us assume that,

x be the number  of tickets sold at Rs.250.

y be the number of tickets sold at Rs.350

We can frame the linear equation for the given conditions as,

x + y = 180 ..........(1)

250 x + 350 y =49000 .........(2)

Step 1:Calculating the  number of tickets at the rate Rs.250 and Rs.350.

Multiplying equation (1) by 250 we get

250 x + 250 y = 45000........(3)

Now subtract equation (3) from Equation (2) we get

100 y = 4000

→y = 40.

Substitute  y  = 40 in equation (1) we will get,

x + 40 = 180.

→ x = 140

Step 2 :Calculating the No:of tickets sold at Rs.300.

No:of tickets = $\frac{collection sum}{rate per ticket}$

→No:of tickets = $\frac{49000}{300}$

→No:of tickets = 163

Therefore, the No:of tickets sold at Rs.250,Rs.350 and Rs.300 are 140,40 and 163 .

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