The cost of car is `400%` greater than the cost of a bike . If there is an increase in the cost of the car is `15%`and that of bike is `20%`. Then the total increase in the cost of the 5 cars and 10 bikes is :

Options

A. `17.5%`
B. `16 3/7 %`
C. `18.5%`
D. `18.25%`

Answer

To solve the problem step by step, we will first determine the cost of the bike, then calculate the cost of the car based on the percentage increase, and finally compute the total increase in cost for 5 cars and 10 bikes.

### Step 1: Define the cost of the bike
Let the cost of the bike be \( x \).

### Step 2: Calculate the cost of the car
The cost of the car is 400% greater than the cost of the bike. This means the cost of the car can be calculated as:
\[ \text{Cost of Car} = \text{Cost of Bike} + 400\% \text{ of Cost of Bike} \]
\[ \text{Cost of Car} = x + 4x = 5x \]

### Step 3: Calculate the increase in the cost of the car
The cost of the car increases by 15%. Therefore, the increase in the cost of the car is:
\[ \text{Increase in Cost of Car} = 15\% \text{ of } 5x = \frac{15}{100} \times 5x = 0.75x \]

### Step 4: Calculate the increase in the cost of the bike
The cost of the bike increases by 20%. Therefore, the increase in the cost of the bike is:
\[ \text{Increase in Cost of Bike} = 20\% \text{ of } x = \frac{20}{100} \times x = 0.2x \]

### Step 5: Calculate the total increase in cost for 5 cars and 10 bikes
Now, we will calculate the total increase in cost for 5 cars and 10 bikes:
- Total increase for 5 cars:
\[ \text{Total Increase for Cars} = 5 \times \text{Increase in Cost of Car} = 5 \times 0.75x = 3.75x \]
- Total increase for 10 bikes:
\[ \text{Total Increase for Bikes} = 10 \times \text{Increase in Cost of Bike} = 10 \times 0.2x = 2x \]

### Step 6: Calculate the overall total increase
Now, we add the total increase for cars and bikes:
\[ \text{Total Increase} = \text{Total Increase for Cars} + \text{Total Increase for Bikes} = 3.75x + 2x = 5.75x \]

### Final Answer
The total increase in the cost of 5 cars and 10 bikes is \( 5.75x \).

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