The charges for renting an SUV vary with the distance travelled by it, apart from a fixed cost of Rs1000.. Charges start from Rs15/km and reduce by Rs1 for every 10 km travelled. If a customer was charged Rs1606 for renting a SUV, what was the distance he travelled by it ?(in km)

Options

A. 38
B. 36
C. 48
D. 46

Answer

To find the distance travelled by the customer who was charged Rs. 1606 for renting the SUV, we can break down the problem step by step.

### Step 1: Understand the total charge
The total charge for renting the SUV is Rs. 1606. This total charge includes a fixed cost of Rs. 1000 plus the variable cost based on the distance travelled.

### Step 2: Calculate the variable cost
To find the variable cost, we subtract the fixed cost from the total charge:
\[ \text{Variable Cost} = \text{Total Charge} - \text{Fixed Cost} = 1606 - 1000 = 606 \]

### Step 3: Set up the cost structure
The cost per kilometer starts at Rs. 15/km and decreases by Rs. 1 for every 10 km travelled. We can express the cost per kilometer as:
- For the first 10 km: Rs. 15/km
- For the next 10 km (11 to 20 km): Rs. 14/km
- For the next 10 km (21 to 30 km): Rs. 13/km
- And so on...

### Step 4: Determine the distance travelled
Let \( d \) be the total distance travelled in kilometers. The cost structure can be broken down into segments of 10 km.

1. For the first 10 km, the cost is:
\[ 10 \times 15 = 150 \]
2. For the next 10 km (11 to 20 km), the cost is:
\[ 10 \times 14 = 140 \]
3. For the next 10 km (21 to 30 km), the cost is:
\[ 10 \times 13 = 130 \]
4. For the next 10 km (31 to 40 km), the cost is:
\[ 10 \times 12 = 120 \]
5. For the next 10 km (41 to 50 km), the cost is:
\[ 10 \times 11 = 110 \]
6. For the next 10 km (51 to 60 km), the cost is:
\[ 10 \times 10 = 100 \]

### Step 5: Calculate cumulative costs
Now, we can calculate the cumulative costs for each segment until we reach or exceed the variable cost of Rs. 606.

- Total cost for 10 km: Rs. 150
- Total cost for 20 km: Rs. 150 + Rs. 140 = Rs. 290
- Total cost for 30 km: Rs. 290 + Rs. 130 = Rs. 420
- Total cost for 40 km: Rs. 420 + Rs. 120 = Rs. 540
- Total cost for 50 km: Rs. 540 + Rs. 110 = Rs. 650

At this point, we see that:
- The cost for 40 km is Rs. 540 (less than Rs. 606).
- The cost for 50 km is Rs. 650 (more than Rs. 606).

### Step 6: Calculate the remaining distance
Since the cost for 40 km is Rs. 540, we need an additional:
\[ 606 - 540 = 66 \]
Now, we need to find out how many kilometers can be travelled at Rs. 11/km (the rate for the next segment, which is from 41 km to 50 km).

### Step 7: Calculate the distance at Rs. 11/km
To find the distance travelled at Rs. 11/km:
\[ \text{Distance} = \frac{\text{Remaining Cost}}{\text{Rate}} = \frac{66}{11} = 6 \text{ km} \]

### Step 8: Total distance travelled
Adding this to the previous 40 km:
\[ \text{Total Distance} = 40 + 6 = 46 \text{ km} \]

### Final Answer
The distance travelled by the customer is **46 km**.

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