IIFT 2018 Question Paper | Quants

The best way to boost your IIFT prep is to practice the actual IIFT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. In the 2018 IIFT, Quants was a mixed bag of questions of varying difficulty, with some routine questions and the others were very demanding. Some beautiful questions that laid emphasis on Learning ideas from basics and being able to comprehend more than remembering gazillion formulae and shortcuts.

Question 16 : Land Cruiser Prado, the latest SUV from Toyota Motors, consumes diesel at the rate of \\frac{1}{400}\left\{\frac{1000}{x}+x\right\}) litres per Km. when travelling at the speed of x km/hr. The diesel costs Rs. 65 per litre and the driver is paid Rs. 50 per hour. Find the steady speed that will minimize the total cost of a 1000 km trip?

1. 33 km/hr
2. 36 km/hr
3. 39 km/hr
4. 52 km/hr

Explanatory Answer

Let the optimum speed be v km/hr
Total fuel cost = (1/400)[ (1000/v) + v ] x 1000 x 65 rupees
= 162.5[ (1000/v) + v ]
Total journey time = 1000/v
Total driver cost = 1000 x 50/v
Total cost = 162.5[ (1000/v) + v ] + 1000 x 50/v
= 162.5v + 212500/v
Differentiating total cost wrt v and equating it to zero
162.5 -212500/v² = 0
= > v² = 1307
= > v = 36 km/hr

The answer is '36 km/hr'

Choice B is the correct answer.