Question

The entry fee for a musical concert was Rs. 1, later it was reduced by 20% which increased the net collection of the amount by 40%. The increase in the number of visitors is

Answer 1

Answer: 75 %

Step-by-step explanation:

Let the initial number of visitors in the concert = x

If the entry fee is 1 rupees .

Then the initial collection = 1 x

Now, when the entry fees is reduced by 20%

Then the final entry fee per person = 80 % of 1 = 0.8 rupees.

If the final number of the visitors = y

Then, the total final collection = 0.8 y

According to the question,

The final collection is 40% more than initial collection.

⇒ $0.8 y =\text{ 140\% of 1x}$

⇒ $0.8 y = 1.4 x$

⇒ $y = \frac{1.4x}{0.8}$

⇒ $y = \frac{7x}{4}$

Thus, the increment in the number of visitors

= $\frac{\frac{7x}{4}-x}{x} \times 100$

= $\frac{\frac{7x-4x}{4}}{x} \times 100$

= $\frac{3}{4}\times 100$

= $0.75$

= $75\%$

Therefore, there is an increment of 75% in the number of visitors.

Answer 2

Answer:

75% increase

Step-by-step explanation:

Define x:

Let x be the original number of tickets sold

Find the original revenue:

Ticket = Rs 1

Total Revenue = Rs 1x

Find the Price of the ticket after reduction:

Reduction = 20% of 1 = Rs 0.2

Price after reduction = 1 - 0.2 = Rs 0.80

Find earning after reduction:

Increase = 40% of Rs 1x

increase = 0.4(1x) = 0.4x

Earnings = 1x + 0,4x = Rs 1.4x

Find the number of tickets sold:

Tickets sold = 1.4x ÷ 0.8 = 1.75x

Find the increase:

Increase = 1.75x - x = 0.75x

percentage increase = (0.75x ÷ x ) x 100 = 75%

Answer: 75% increase