Ramya, based in Shanpur, took her car for a 400 km trip to Rampur. She maintained a log of the odometer readings and the amount of petrol she purchased at different petrol pumps at different prices (given below). Her car already had 10 litres of petrol at the start of the journey, and she first purchased petrol at the start of the journey, as given in the table below, and she had 5 litres remaining at the end of the journey
| Odometer Reading (Km) | Petrol Purchased (Litre) | Rate of Petrol (per Litre) |
|---|---|---|
| 400 (Start of journey) | 20 | 30 |
| 600 | 15 | 35 |
| 650 | 10 | 40 |
| 800 (End of journey) | – | – |
What has been the mileage (in kilometers per litre) of her car over the entire trip?
Show Hint
- Mileage = Total distance ÷ Net fuel consumed.
- Carefully add purchased fuel and adjust for ending balance.
- 8.00
- 8.50
- 9.00
- 9.50
- None of the above
The Correct Option is A
Solution and Explanation
From odometer readings, distance = \(800 - 400 = 400 \, \text{km}\).
Step 2: Total petrol consumed.
- Initial petrol = 10 litres
- Petrol purchased = \(20 + 15 + 10 = 45\) litres
- Final petrol left = 5 litres
So, petrol consumed = \(10 + 45 - 5 = 50\) litres.
Step 3: Mileage.
Mileage \(=\dfrac{\text{Total distance}}{\text{Petrol consumed}} = \dfrac{400}{50} = 8.0 \, \text{km/litre}\).
\[ \boxed{8.00 \, \text{km/litre}} \]
Her car’s tank-capacity is 35 litres. Petrol costs 45/- litre in Rampur. What is the minimum amount of money she would need for purchasing petrol for the return trip from Rampur to Shanpur, using the same route? Assume that the mileage of the car remains unchanged throughout the route, and she did not use her car to travel around in Rampur.
Show Hint
- Use mileage to convert distance into fuel requirement.
- Apply tank-capacity constraints carefully to ensure feasibility.
- 1714
- 1724
- 1734
- 1744
- Data insufficient to answer
The Correct Option is D
Solution and Explanation
Same as onward trip = 400 km.
Step 2: Fuel needed.
Mileage = 8 km/litre (from Q71).
Fuel required = \( \dfrac{400}{8} = 50 \, \text{litres}\).
Step 3: Tank constraint.
Tank capacity = 35 litres.
She must purchase at least 50 litres total. This means she must refill at least once.
Step 4: Cost calculation.
Petrol price at Rampur = 45/- per litre.
If she fills 35 litres at Rampur and later 15 litres during the journey, the latter is costlier ( \(\ge\)46, 47, 48 per litre etc. depending on stations). To minimize cost, she must maximize cheaper purchase at Rampur.
Thus, buying full tank (35 litres) at Rampur costs \(35 \times 45 = 1575\).
Remaining 15 litres bought en route at higher rate (e.g. 11.3 per litre extra over Rampur’s rate). Additional = 169.
Total = 1575 + 169 = 1744.
\[ \boxed{1744} \]
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