IIFT 2019

Nawab’s satisfaction/ utility level is given by adding twice of the satisfaction level of Saif with the satisfaction level of Amir.

Saif makes a profit of ₹ 100, his satisfaction level goes up by 10% and if he suffers a loss of ₹100, his satisfaction level goes down by 10%.

Amir makes profit of ₹ 100, his satisfaction level goes up by 5% and if he suffers a loss of ₹ 100, his satisfaction level goes down by 15%.

Nawab’s satisfaction level is 24 and the satisfaction level of Saif is the same as the satisfaction level of Amir

Let x be the satisfaction level of Saif 

24=3x

x=8

If Saif makes a profit of 100 and Amir suffers a loss of ₹ 100, the satisfaction level of Saif and Amir goes up by 10% and goes down by 15% respectively.

The satisfaction of Saif and Amir = 8.8 and 6.8

Nawab's new satisfaction/ utility level = 2*8.8+6.8 =24.4

Percentage change = $$\ \frac{\ 24.4-24}{24}$$

=1.67%

D is the correct answer.

Let 'a' and 'b' be the heights of the two poles

X be the initial position of the man and the angles of elevation be $$60^0$$ and $$45^0$$

Distance between pole 1 and X  = $$\ \frac{\ a}{\sqrt{\ 3}}$$ and distance between pole 2 and X = b

Let Y be the position of the man after walking sometime towards the other pole = 

Distance between Y and pole 1 = $$\ \ a\sqrt{\ 3}$$ and distance between the pole 2 and Y = $$\ \frac{\ b}{\sqrt{\ 3}}$$

Since the distance between the poles will remain the same 

$$\ \frac{\ a}{\sqrt{\ 3}}$$ + b = $$\ \ a\sqrt{\ 3}$$ + $$\ \frac{\ b}{\sqrt{\ 3}}$$

$$\ \frac{\ a}{b}=\ \ \frac{\ \sqrt{\ 3}-1}{2}$$
A is the correct answer.

Consider the revenue per passenger = P

=> Total revenue = 24*4P = 96P

Since the total cost is proportional to interest, it can be assumed as 120*K

Total cost*(1+Profit/100)=Revenue 

=> 120K(1+15/100) = 96P ..........(1)

New Revenue = 20*5P = 120*(0.9)K*(1+Profit/100) ..........(2)

Dividing (2) by (1),

25/24  = (0.9/1.15)(1+Profit/100)

Profit/100 = (25*23)/(18*24) - 1 = 1.33-1

=> Profit = 33%, Option A is the answer.

The number of students in 2018-19 MBA batch = 400

Number of students who did not choose 'Business Statistics' = 200

Number of students who did not choose 'International Management' = 100

Number of students who did not choose any of the two subjects = 80

Number of students who choose at least one of the two subjects = 400-80=320

140+x=320

x=320-140=180

A is the correct answer.

Time when the tho hands of the clock are completely opposite to each other between 2.00 pm and 3.00 pm

let x be the minutes covered in between 2.00 pm and 3.00 pm

180=$$\frac{11x-60*2}{2}$$

x=43.6

B is the correct answer.

Option A: 

$$37^{371}-26^{371}$$ mod 10

=$$7^{371}-6^{371}$$

Since 7 and 10 are co-prime to each other

E(10) = 10*($$\left(1-\ \frac{\ 1}{2}\right)\left(1-\ \frac{\ 1}{5}\right)$$

=4

$$7^{4}$$ mod 10 = 1

$$7^{4*92}*7^{3}$$ mod 10 = $$1*7^{3}$$ mod 10 =3

$$6^{371}$$ mod 10 = 0

Hence $$37^{371}-26^{371}$$ is not divisible by 10

Option B: 

$$37^{371}-26^{371}$$ mod 11

$$4^{371}-4^{371}$$ mod 11

Hence $$37^{371}-26^{371}$$ is divisible by 11

Option C: 

$$37^{371}-26^{371}$$ mod 12

$$1^{371}-2^{371}$$ mod 12

Hence $$37^{371}-26^{371}$$ is not divisible by 12

Option D:

$$37^{371}-26^{371}$$ mod 15

$$7^{371}-11^{371}$$ mod 15

$$37^{371}-26^{371}$$ is not divisible by 15

B is the correct answer.

Let the speed of the boat in the still water = 100x and the travel time = 100t and the distance between Rishikesh and Haridwar be 'd'

Let the speed of the river be 100r

Since the owner of the motorboat decides to increase the number of trips, he increased the speed.

Increased speed in still water = 150x

Final travel time = 40t

$$\ \frac{\ d}{100x+100r}+\ \frac{\ d}{100x-100r}=100t$$   ---(1)

After the ease in speed 

$$\ \frac{\ d}{150x+100r}+\ \frac{\ d}{150x-100r}=40t$$     ---(2)

Dividing 1 by 2, we get x/r = $$\sqrt{\ \ \frac{\ 11}{6}}$$

A is the correct answer.

The average scores of Virat, Rohit, Mahendra, Rahul and Shikhar in the first 20 matches are 60, 55, 50, 45,40 respectively.

In the next 10 matches, Virat and Rohit each scored 900 runs whereas Mahendra scored twice that of Rahul.

Virat's score in 30 matches = 60*20+900=2100

Let us consider Rahul scored x runs in last 10 matches, then Mahendra scores 2x runs.

Rahul's score in 30 matches = 45*20+x=900+x

Mahendra's score in 30 matches = 50*20+2x = 1000+2x

It is given that 

After 30 matches, Virat’s new average score is twice that of Rahul.

2100=2(900+x)

x=150

Mahendra's score in 30 matches =1300

Average score of Mahendra = 43

C is the correct answer.

From the above figure area of  the region bounded by ABCDEFGH = Are of the square with side 2 - (4*quadrants with side 1cm + 4x)

=4-$$\pi\ $$-4x

Which is same as the area of the square with side 1 cm -4y

4-$$\pi\ $$-4x = 1-4y

4x-4y=3-$$\pi$$

y-x= $$\frac{\pi-3}{4}$$

D is the correct answer.

Let the capacity of the cistern be LCM of 12 and 15 = 60l

The rate of flow through the inlet pipe 1 = 60/12=5 l/min

The rate of flow through the inlet pipe 2 = 60/15=4 l/min

It is given that despite leakage the two inlet pipes together can fill the cistern in 20 min.

Let the flow through the leakage be x l/min

(5+4-x)20=60

9-x=3

x=6

The leakage will empty the cistern in 60/6=10 min

A is the correct answer.