Question Details

The line graph given below shows total number of people (male + female) visited four different parks (A, B, C and D) and table shows fraction of male out of total people visited these four parks.
Read the data carefully and answer the questions below.
If there is discount of 20% on each ticket for females as compare to male and total revenue received by park D from all the people is Rs 2280, then find the price of each ticket for female.

Options

20 Rs

25 Rs

24 Rs

12 Rs

30 Rs

Show Answer

Correct Answer :

Option A

20 Rs

Solution :

Correct Answer: 20 Rs

Step-by-Step Explanation:

Step 1: Analyze the Line Graph and Table
Let us first analyze the line graph to determine the total number of people (male + female) who visited the parks:

The vertical axis is labeled at intervals of 32 units: 0, 32, 64, 96, 128, 160. Between any two main grid lines (which represent a difference of 32), there are 4 subdivisions. Therefore, the value of each smaller grid line is:
$\frac{32}{4} = 8$
Using this grid scale, we find the total number of people visited for each park:
- Park A: Two grid lines above 128 = $128 + 2 \times 8 = 144$
- Park B: Exactly at the line of 160 = $160$
- Park C: Two grid lines above 96 = $96 + 2 \times 8 = 112$
- Park D: Exactly at the line of 96 = $96$

Next, let us refer to the table showing the fraction of males:

For Park D, the fraction of males out of the total visitors is $\frac{3}{4}$ .

Step 2: Calculate the Number of Males and Females in Park D
The total number of visitors in Park D is 96.
Number of males in Park D:
$Males = 96 \times \frac{3}{4} = 72$
Number of females in Park D:
$Females = 96 - 72 = 24$

Step 3: Setup the Revenue Equation
Let the price of each ticket for a male be $P_{m}$ Rs.
Since there is a 20% discount on tickets for females compared to males, the price of a female ticket $P_{f}$ is:
$P_{f} = P_{m} \times (1 - 0.20) = 0.8 P_{m}$
The total revenue collected from Park D is Rs 2280. We can express this relationship as:
$(Number of Males \times P_{m}) + (Number of Females \times P_{f}) = 2280$
Substituting the known values:
$72 P_{m} + 24 (0.8 P_{m}) = 2280$
$72 P_{m} + 19.2 P_{m} = 2280$
$91.2 P_{m} = 2280$
$P_{m} = \frac{2280}{91.2} = 25$

Step 4: Find the Ticket Price for a Female
Using the value of the male ticket price ( $P_{m} = 25$ Rs):
$P_{f} = 0.8 \times 25 = 20 Rs$
Thus, the price of each ticket for a female is 20 Rs.