Question

$\huge{\boxed{{Question}}}$

In an auditorium, 300 tickets were sold. The total sale of tickets was ₹1250. If the tickets were of two denominations of ₹2.50 and ₹5.00. How many of each denomination were sold.​​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

In an auditorium, 300 tickets were sold. The total sale of tickets was ₹1250.

The tickets were of two denominations of ₹2.50 and ₹5.00.

Let assume that

The tickets of denomination ₹ 2.50 sold be x

and

The tickets of denomination of ₹ 5 sold be y.

So, According to first condition, total tickets sold = 300

$\rm \: x + y = 300$

$\rm\implies \:x = 300 - y - - - - (1)$

Now, According to second condition, The total sale of tickets was ₹1250, if the tickets were of two denominations of ₹2.50 and ₹5.00.

Amount collected on selling x tickets of ₹ 2.5 be 2.5x

and

Amount collected on selling y tickets of ₹ 5 be 5y.

Total amount collected = ₹ 1250

$\rm \: 2.5x + 5y = 1250$

$\rm \: \frac{5}{2} x + 5y = 1250$

On dividing both sides by 5, we get

$\rm \: \frac{1}{2} x + y = 250$

On multiply by 2, we get

$\rm \: x + 2y = 500$

On substituting the value of x from equation (1), we get

$\rm \: 300 - y + 2y = 500$

$\rm \: 300 + y = 500$

$\rm \: y = 500 \: - \: 300$

$\rm\implies \:y = 200$

On substituting the value of y, in equation (1), we get

$\rm \: x= \: 300 - 200$

$\rm \: = \: 300 - 200$

$\rm \: = \: 100$

Hence,

The tickets of denomination ₹ 2.50 sold be 100

and

The tickets of denomination of ₹ 5 sold be 200

Answer 2

Answer:

Given :-

• In an auditorium, 300 tickets were sold.
• The total sale of tickets was Rs 1250.
• The tickets were of two denominations of Rs 2.50 and Rs 5.00.

To Find :-

• How many of each denomination were sold.

Solution :-

Let,

➳ The number of tickets of denomination of Rs 2.50 be x

➳ The number of tickets of denomination of Rs 5.00 will be (300 - x)

Now,

$\bigstar$ The amount spent on Rs 2.50 tickets :

$\implies \sf Rs\: 2.50 \times x$

$\implies \sf\bold{\blue{Rs\: 2.50x}}$

Again,

$\bigstar$ The amount spent on Rs 5 tickets :

$\implies \sf Rs\: 5 \times (300 - x)$

$\implies \sf Rs\: 5(300 - x)$

$\implies \sf\bold{\blue{Rs\: 1500 - 5x}}$

According to the question :

$\bigstar$ The total sale of tickets was Rs 1250.

So,

$\implies \sf 2.50x + 1500 - 5x =\: 1250$

$\implies \sf 1500 - 1250 =\: - 2.50x + 5x$

$\implies \sf 250 =\: 2.50x$

$\implies \sf \dfrac{250}{2.50} =\: x$

$\implies \sf 100 =\: x$

$\implies \sf\bold{\purple{x =\: 100}}$

Hence, the required each denomination were sold are :

✯ Number of tickets of denomination of Rs 2.50 :

$\implies \sf Number\: of\: tickets\: of\: Rs\: 2.50 =\: x$

$\implies \sf\bold{\red{Number\: of\: tickets\: of\: Rs\: 2.50 =\: 100}}$

✯ Number of tickets of denomination of Rs 5 :

$\implies \sf Number\: of\: tickets\: of\: Rs\: 5\: =\: (300 - x)$

$\implies \sf Number\: of\: tickets\: of\: Rs\: 5\: =\: (300 - 100)$

$\implies \sf\bold{\red{Number\: of\: tickets\: of\: Rs\: 5 =\: 200}}$

$\therefore$ The number of tickets of denomination of Rs 2.50 is 100 and the number of tickets of denomination of Rs 5 is 200 .