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The question is from the topic of Time Speed and Distance. This is relatively a straightforward question and only tests the basic concepts. Time Speed and Distance is a favorite in CAT Exam and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 16: Ramesh takes 6.5 hours to go from city A to city B at 3 different speeds 30 kmph, 45 kmph, and 60 kmph covering the same distance with each speed. The respective mileages per liter of fuel are 11 km, 14 km and 18 km for the above speeds. Ramesh's friend Arun is an efficient driver and wants to minimise his friend's car's fuel consumption. So he decides to drive Ramesh's car one day from city A to city B. How much fuel will he be able to save?

  1. 4.2 liters
  2. 4.5 liters
  3. 0.7 liters
  4. 0.3 liters

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Explanatory Answer

Method of solving this CAT Question from Time Speed Distance: Finding the total distance travelled is the key to answer this question.

Total time = 6.5 hrs
Let the total distance be x
Ramesh's speeds = 30, 45, 60 kmph

6.5 = \\frac{x/3}{30}\\) + \\frac{x/3}{45}\\) + \\frac{x/3}{60}\\)
6.5 = \\frac{2x+4x/3+x}{180}\\)
6.5 = \\frac{6x+4x+3x}{540}\\)
or x = 270 km

With each speed distance covered = 270/3 = 90 km
Fuel consumed when driving at 30 = 90/11 = 8.1 l
Fuel consumed when driving at 45 = 90/14 = 6.4 l
Fuel consumed when driving at 60 = 90/18 = 5
Total fuel = 8.1 + 6.4 + 5 = 19.5 liters

When Arun drives the car, he should drive at 60 kmph throughout so that he gets the maximum mileage!
Fuel consumption when driving at 60 for entire journey = 270/18 = 15 liters

The question is " So he decides to drive Ramesh's car one day from city A to city B. How much fuel will he be able to save? "
Difference = 19.5 – 15 = 4.5

Hence, the answer is 4.5 liters.

Choice B is the correct answer.


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