Ticket for an adult is Rs 500 and a child is Rs 200. 1 child goes free with two adults. If a group has 20 adults and 8 children what will be the discount the group get ?

Options

A. a)0.5343
B. b)0.1379
C. c)0.322
D. d)0.3506

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the total ticket price for adults and children.
- The ticket price for one adult is Rs 500.
- The ticket price for one child is Rs 200.
- The group has 20 adults and 8 children.

**Calculation:**
- Total price for adults = Number of adults × Price per adult
\[ = 20 \times 500 = 10000 \text{ Rs} \]
- Total price for children = Number of children × Price per child
\[ = 8 \times 200 = 1600 \text{ Rs} \]
- Total fare for the group = Total price for adults + Total price for children
\[ = 10000 + 1600 = 11600 \text{ Rs} \]

### Step 2: Determine how many children can go free.
- According to the scheme, 1 child goes free with every 2 adults.
- For 20 adults, the number of free children = Number of adults / 2
\[ = 20 / 2 = 10 \text{ children} \]

### Step 3: Calculate the discount received.
- The group has 8 children, and since they can take advantage of the free child policy, all 8 children can go free.
- The discount is the total price of the free children's tickets.

**Calculation:**
- Discount = Number of free children × Price per child
\[ = 8 \times 200 = 1600 \text{ Rs} \]

### Step 4: Calculate the percentage of the discount.
- To find the percentage discount, use the formula:
\[ \text{Discount Percentage} = \left( \frac{\text{Discount}}{\text{Total Fare}} \right) \times 100 \]

**Calculation:**
- Discount Percentage = \( \left( \frac{1600}{11600} \right) \times 100 \)
\[ = \left( \frac{1600}{11600} \right) \times 100 \approx 13.79\% \]

### Final Answer:
The discount the group gets is approximately **13.79%**.

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