IIFT 2019 Question Paper | Quants

CAT Questions

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 2019 IIFT, quants were 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 23: Nawab has two sons Saif and Amir who have export businesses. Nawab's satisfaction/ utility level is given by adding twice of the satisfaction level of Saif with the satisfaction level of Amir. If Saif makes a profit of Rs 100, his satisfaction level goes up by 10% and if he suffers a loss of Rs 100, his satisfaction level goes down by 10%. If Amir makes profit of Rs 100, his satisfaction level goes up by 5% and if he suffers a loss of Rs 100, his satisfaction level goes down by 15%. Currently, Nawab's satisfaction level is 24 and the satisfaction level of Saif is the same as the satisfaction level of Amir. If Saif makes a profit of 100 and Amir suffers a loss of Rs 100, what is the approximate percentage change in Nawab's satisfaction level?

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Video Explanation

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Explanatory Answer

Let the satisfaction level of Nawab, Saif and Amir be n, s and a respectively.
s = a and 2s + a = n = 24
Therefore, a = s = 8
New satisfaction level of Saif = 1.1 x 8 = 8.8 [due to profit of 100] 
New satisfaction level of Amr = 0.85 x 8 = 6.8 [due to loss of 100]
New Satisfaction level of Nawab = 2 x 8.8 + 6.8 = 24.4

Percentage change = 0.4 x \\frac{100}{24}) = 1.66%

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The question is "What is the approximate percentage change in Nawab's satisfaction level?"

Hence, the answer is, "1.66%"