The cost of servicing of a maruti car at Maruti care Pvt. Ltd. is ₹ 400 Manager of service centre told me that for the second service within a year a customer can avail a `10%` discount and further for third and fourth servicing he can avail `10%` discount of the previous amount paid, within a year. Further if a customer gets more than 4 services within a year he has to pay just `60%` of the servicing charges on these services. A customer availed 5 services from the same servicing station, what is the total percentage discount fetched by the customer?

Options

A. `19.42%`
B. `18.5%`
C. `17.6%`
D. `26%`

Answer

To solve the problem step by step, let's break down the costs and discounts for each of the five services availed by the customer.

### Step 1: Determine the cost of the first service.
The cost of servicing the Maruti car is ₹400. Since the first service does not have any discount, the cost remains:
- **Cost of 1st service = ₹400**

**Hint:** The first service is always at full price.

### Step 2: Calculate the cost of the second service after applying the discount.
For the second service, a 10% discount is applicable:
- Discount = 10% of ₹400 = 0.10 × ₹400 = ₹40
- Cost of 2nd service = ₹400 - ₹40 = ₹360

**Hint:** Remember to calculate the discount based on the original price.

### Step 3: Calculate the cost of the third service after applying the discount.
For the third service, a 10% discount is applied to the amount paid for the second service:
- Discount = 10% of ₹360 = 0.10 × ₹360 = ₹36
- Cost of 3rd service = ₹360 - ₹36 = ₹324

**Hint:** The discount for the third service is based on the cost of the second service.

### Step 4: Calculate the cost of the fourth service after applying the discount.
For the fourth service, again a 10% discount is applied to the amount paid for the third service:
- Discount = 10% of ₹324 = 0.10 × ₹324 = ₹32.40
- Cost of 4th service = ₹324 - ₹32.40 = ₹291.60

**Hint:** Keep applying the discount to the previous service's cost.

### Step 5: Calculate the cost of the fifth service.
For the fifth service, since the customer has availed more than four services, they only pay 60% of the original service charge:
- Cost of 5th service = 60% of ₹400 = 0.60 × ₹400 = ₹240

**Hint:** For more than four services, the cost is a fixed percentage of the original price.

### Step 6: Calculate the total cost for all five services.
Now, we sum up the costs of all five services:
- Total cost = Cost of 1st + Cost of 2nd + Cost of 3rd + Cost of 4th + Cost of 5th
- Total cost = ₹400 + ₹360 + ₹324 + ₹291.60 + ₹240 = ₹1615.60

**Hint:** Make sure to add all the costs together accurately.

### Step 7: Calculate the total discounts received.
Now, let's calculate the total discounts:
- Total original cost without any discounts = ₹400 × 5 = ₹2000
- Total discounts = Total original cost - Total cost
- Total discounts = ₹2000 - ₹1615.60 = ₹384.40

**Hint:** The total discount is the difference between the original total and the final total.

### Step 8: Calculate the total percentage discount.
To find the total percentage discount:
- Total percentage discount = (Total discounts / Total original cost) × 100
- Total percentage discount = (₹384.40 / ₹2000) × 100 = 19.22%

**Hint:** Use the formula for percentage to find the discount percentage.

### Final Answer:
The total percentage discount fetched by the customer is **19.22%**.