Question

Auto fare in Bombay is ₹2.40 for the first 1 km, ₹2.00 per km for the next 4 km, and ₹1.20 for each additional km thereafter. Find the fare in rupees for \(k\) km (\(k \geq 5\)).

• A. \(2.4 + 1.2(2k - 3)\)
• B. \(10.4 + 1.2(k - 5)\)
• C. \(2.4 + 2(k - 3) + 1.2(k - 5)\)
• D. \(10.4 + 1.2(k - 4)\)

Hint:

Break tiered pricing problems into slabs and compute fixed cost first, then add variable cost for remaining units.

Answer 1

The Correct Option is B

Step 1: Fare breakdown
- First 1 km = ₹2.40 - Next 4 km = ₹2.00 per km → ₹2 × 4 = ₹8.00 - So, first 5 km total = ₹2.40 + ₹8.00 = ₹10.40 Step 2: Additional fare beyond 5 km
Every km after 5 km is charged at ₹1.20 So, for \(k > 5\), additional kms = \(k - 5\) Step 3: Final fare \[ \text{Total fare} = 10.4 + 1.2(k - 5) \]