IIFT 2015 Question Paper

Distance = Speed x Time

In morning slot, Let speed be S and time taken be T, then distance covered = ST

Then, in evening slot, speed will be 1.5S and time taken will be 1.5T, then distance covered = 2.25ST

Average Speed = $$\frac{Total \space distance \space covered}{Total \space time \space taken}$$

For entire journey, average speed is: 

Average Speed =$$\frac{ST + 2.25ST}{T + 1.5T}$$ = $$\frac{3.25ST}{2.5T}$$ = 1.3S

For morning, Average Speed is S.

Hence, the average speed of the bus for the entire journey is greater than its average speed in the morning by 30%

The radius of sphere is 8 $$cm$$. Then applying Pythagoras, the radius of base of cylinder is $$\sqrt{15}$$  $$cm$$

The height of cylinder is given as 14 $$cm$$. Volume of cylinder is $$\pi$$ $$r^{2}$$h 

$$\frac{22}{7}$$* 15*14 = 660 $$cm^3$$

Seema saved Rs. 900 in the first 3 months. She must saved Rs. (11400 - 900) = Rs. 10500 in the subsequent months.

The sequence will be of the form: 350 + 400 +........... $$n$$ terms = 10500

=> $$\frac{n}{2}$$ [2*350 + ($$n$$-1)*50] = 10500

=> $$\frac{n}{2}$$ [70 + ($$n$$-1)5] = 1050

=> $$n^{2}$$ + 13$$n$$ = 420

Solving, we get $$n$$ = 15

The savings of Rs. 10500 is done in 15 months. Seema saved Rs. 11400 in 15+3 = 18 months.

Hence, option C is the correct answer.

Let total sales be 'x'

The commission that Sailesh will get is x - 265000

He gets 6% on sales upto 100000 and 5% on sales greater than that.

Calculating his commission on total sales:

0.06*100000 + 0.05(x-100000)

Equating, 

0.05x + 1000 = x - 265000

0.95x = 266000

x= 280000

Hence, his sales were worth 280,000

P is doing a job in 42 days. In one day, he does 1/42 of the work.

Q is more efficient than P by 26%.

Then, the part of work that Q does in one day is: $$\frac{1}{42}$$ x 1.26 = 3/100

R is more efficient than Q by 50%.

Then, the part of work that R does in one day is: $$\frac{3}{100}$$ x 1.5 = 9/200

If Q and R are put together then part of work they will finish in a day is:

$$\frac{3}{100}$$ + $$\frac{9}{200}$$ = $$\frac{15}{200}$$ 

Hence total work can be done in 200/15 = 13.33 days $$\cong$$ 13 days  

Composition of alloy P

Silver:Copper:Aluminium = 45:0:55

Composition of alloy Q

Silver:Copper:Aluminium = 30:35:35

They are mixed in ratio of 1: 4.5

Let us consider alloy P is taken 200 grams and alloy Q is taken 900 grams.

Then for alloy P :-

Silver:Copper:Aluminium = 90:0:110

For alloy Q:

Silver:Copper:Aluminium = 270:315:315

Total weight of P and Q combined is 1100 grams.

When P and Q are mixed, the new combined ratio of 

Silver:Copper:Aluminium = 360:315:425

Percentage of Silver in mixture = $$\frac{360}{1100}$$ x 100 $$\cong$$ 33%

Percentage of Copper in mixture = $$\frac{315}{1100}$$ x 100 $$\cong$$ 29%

The starting position of ladder is AB.

AB = 7.6 cm and OB = 6.4 cm

Applying Pythagoras Theorem in $$\triangle$$ AOB

$$OA^{2}$$ + $$OB^{2}$$ = $$AB^{2}$$

OA = 4.10 cm

Now ladder top slips by 1.2 cm, the new position of ladder becomes A'B'

OA' = 4.10 - 1.2 = 2.9 cm

Applying Pythagoras Theorem in $$\triangle$$ A'OB'

$$OA'^{2}$$ + $$OB'^{2}$$ = $$A'B'^{2}$$

OB' = 7.02 cm

 Hence, the foot of the ladder is shifted by approximately OB' - OB = 0.6cm

This question can be solved with the help of options easily. 
We can say that 4x - 9 $$\geq$$ 0. Hence x $$\geq$$ 2.25. Now we can check option C and D.

Option C: $$\sqrt{4x - 9}$$ + $$\sqrt{4x + 9}$$ = $$\sqrt{3}$$ + $$\sqrt{21}$$ Which is not same as what we have in the question. Hence, this is not the correct answer. 

Option D: $$\sqrt{4x - 9}$$ + $$\sqrt{4x + 9}$$ = $$\sqrt{7}$$ + $$\sqrt{25}$$ = 5 + $$\sqrt{7}$$. Which is the same as what we have in the question. Hence, we can say that option D the correct answer. 

Simplifying the surds, and writing everything on numerator we get:

= $${(2^{2p + 1/2 + 1/2 + p/2 - 1 + p/2}})^{1/p}$$

= $${(2^{3p}})^{1/p}$$

= $$2^{3}$$ = 8

The probability that the student passes in the first trimester is 0.92

Now given that if the student passes in the first trimester then probability of moving into second second year is 0.87

Hence, the probability of completing first year is 0.92 x 0.87 = 0.80