In a movie theatre, the price of the ticket per kid is $2 while per adult it is $5 . On a particular day, 2000 people bought tickets and an amount of $5,050 was collected. Find the number of $2 tickets sold on that day.
Given:
Price per kid's ticket = $2
Price per adult's ticket = $5
Total people = 2000
Total amount collected = $5,050
Solution:
Let the number of $2 tickets sold be x (kids), and the number of $5 tickets sold be y (adults).
Now, from the condition;
x + y = 2000………(1)
2x + 5y = 5050……(2)
Subtracting 5×eqn(1) – eqn(2)
We get,
3x = 4950
x = ₹1650
Thus, The number of $2 tickets sold is 1,650.
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Assertion (A) | Reason (R) |
The system of equations: | System of equations |
On a particular day each of Danny, Edwin and Fahim sold three types of pens from their respective shops. Danny and Edwin sold an identical number of pens of Type A while Fahim sold twice as many pens of Type A as each of Danny and Edwin sold. The ratio of the numbers of pens of Type B sold by Danny, Edwin and Fahim was 3 : 5 : 2 respectively, while each of the trio sold an identical number of pens of Type C. The three sellers sold each of the types of pens at different prices per unit.
Assertion (A): It is possible that Danny sold each pen of Type A at a profit of Rs each pen of Type B at a loss of Re 1, and each pen of Type C at a loss of Rs 12 and made an overall profit of Rs 125; Edwin sold each pen of Type A at a profit of Rs 2, each pen of Type B at a loss of Rs 6, and each pen of Type C at a profit of Rs 6 and made an overall profit of Rs 110; and Fahim sold each pen of Type A at a profit of Re 1, each pen of Type B at a profit of Re 1, and each pen of Type C at a loss of Rs 3 and made an overall profit of Rs 210.
Reason (R): Framing and solving the three possible linear equations we will find that we get a unique solution.
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