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On the 1st day of the sale of tickets of a drama 35 tickets in all were sold. If the rates of the tickets were Rs.20 and Rs. 40 per ticket and the total collection was Rs. 900.
Find the number of tickets sold of each rate.
Q)
Sol.
Rs. 20 per ticket
Rs. 40 per ticket
Total
No. of Tickets
x
y
35
Collection
20x
40y
900
As per the 1st given condition,
x
+
y
= 35
As per the 2nd given condition,
20x
+
40y
= 900
.......(i)
Dividing throughout by 20, we get
x
+
2y
= 45
........(ii)
Let the number of tickets of Rs.20 be x and the number of tickets of Rs.40 be y
There are two types of tickets.
Rs. 20 tickets
Rs. 40 tickets
Let us understand the sum with the help of a table
No. of tickets: x
No. of tickets: y
How many total tickets sold?
The second condition is about collection.
If I have 2 tickets of Rs. 20, then total collection will be?
20 × 2 = 40
Similarly, If I have 4 tickets of Rs. 20, then total collection will be?
20 × 4 = 80
20 × x = 20x
What is the total collection?
Similarly, If I have y tickets of Rs. 40, then total collection will be?
40 × y = 40y
How many types of tickets are there?
Since we don’t know the number of tickets sold of Rs. 20 and Rs. 40
Let us assume
Similarly, If I have x tickets of Rs. 20, then total collection will be?
What do we have to find?
As per the 1st given condition,
x
+
y
= 35
As per the 2nd given condition,
20x
+
40y
= 900
.......(i)
Dividing throughout by 20, we get
x
+
2y
= 45
........(ii)
Subtracting (ii) from (i),
x + y = 35
x + 2y = 45
– y
∴ y = 10
(–) (–) (–)
Substituting y = 10 in (i),
x
+ 10
= 35
∴
x
=
∴
x
= 25
The number of tickets sold at Rs.20 and Rs.40 each are 25 tickets and 10 tickets respectively.
∴
On the 1st day of the sale of tickets of a drama 35 tickets in all were sold. If the rates of the tickets were Rs.20 and Rs. 40 per ticket and the total collection was Rs. 900.
Find the number of tickets sold of each rate.
(Q)
Sol.
Let the number of tickets of Rs.20 be x and the number of tickets of Rs.40 be y
35
–
10
= – 10