Directions : Read the following and answer the questions that follow.
Two friends Shayam and Kailash own two versions of a car. Shayam owns the diesel version of the car, while Kailash owns the petrol version. Kailash's car gives an average that is 20% higher than Shayam's in terms of litres per kilometer). It is known that petrol costs 60% of its price higher than diesel.
The ratio of the cost per kilometer of Kailash's car to Shayam's car is

Options

A. A)`3:1`
B. B)`1:3`
C. C)`4:1`
D. D)`2:1`

Answer

To solve the problem step by step, we will analyze the information given about the two cars owned by Shyam and Kailash.

### Step 1: Define the Mileage
Let's assume Shyam's car (diesel) has a mileage of \( M_S \) liters per kilometer. According to the problem, Kailash's car (petrol) has a mileage that is 20% higher than Shyam's. Therefore, we can express Kailash's mileage \( M_K \) as:
\[ M_K = M_S + 0.2 \times M_S = 1.2 \times M_S \]

### Step 2: Assign Values to Mileage
For simplicity, let's assume Shyam's car gives a mileage of 5 liters per kilometer:
\[ M_S = 5 \text{ liters/km} \]
Then Kailash's mileage will be:
\[ M_K = 1.2 \times 5 = 6 \text{ liters/km} \]

### Step 3: Define the Cost of Petrol and Diesel
Let the cost of diesel be \( D \) units. According to the problem, petrol costs 60% more than diesel. Therefore, the cost of petrol \( P \) can be expressed as:
\[ P = D + 0.6D = 1.6D \]

### Step 4: Calculate Cost per Kilometer
The cost per kilometer for each car can be calculated using the formula:
\[ \text{Cost per kilometer} = \frac{\text{Cost of fuel}}{\text{Mileage}} \]
For Shyam's car:
\[ \text{Cost per kilometer for Shyam} = \frac{D}{M_S} = \frac{D}{5} \]
For Kailash's car:
\[ \text{Cost per kilometer for Kailash} = \frac{P}{M_K} = \frac{1.6D}{6} \]

### Step 5: Simplify the Cost per Kilometer for Kailash
Now, we simplify the cost per kilometer for Kailash:
\[ \text{Cost per kilometer for Kailash} = \frac{1.6D}{6} = \frac{0.8D}{3} \]

### Step 6: Find the Ratio of Cost per Kilometer
Now, we need to find the ratio of the cost per kilometer of Kailash's car to Shyam's car:
\[ \text{Ratio} = \frac{\text{Cost per kilometer for Kailash}}{\text{Cost per kilometer for Shyam}} = \frac{\frac{0.8D}{3}}{\frac{D}{5}} \]
This can be simplified as follows:
\[ \text{Ratio} = \frac{0.8D}{3} \times \frac{5}{D} = \frac{0.8 \times 5}{3} = \frac{4}{3} \]

### Final Step: Present the Ratio
Thus, the ratio of the cost per kilometer of Kailash's car to Shyam's car is:
\[ \text{Ratio} = \frac{4}{3} \]

### Conclusion
The final answer for the ratio of the cost per kilometer of Kailash's car to Shyam's car is \( 4:3 \).

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