IIFT 23rd Dec 2021 Slot 1

From the above information, we can say that Rahul, Sohan and Ram take 12, 18 and 10 days respectively to complete the work alone.

LCM(12, 18, 10)= 180

Let the total work be 180 units

So Work done by Rahul in 1 day = 15 units

Work done by Sohan in 1 day = 10 units

Work done by Ram in 1 day = 18 units

Let the time taken by Sohan to complete the remaining work be x days.

Therefore, 180 = 3*(15+10+18) + 10x

or, 180 = 129 - 10x

or, x= 5.1 days

Let the cost of 1000gm of dal be rupees 1000

Now the shopkeeper is buying 1100 gm of dal for rupees 1000

While selling 900 gm of dal the shopkeeping is charging the price of 1000 gm

Therefore while selling 1100 gm of dal the shopkeeper will charge the price of (1000/900)*1100 gm = 11000/9 gm

He has marked up the price by 20% and then given a discount of 10%

So price charged by shopkeeper = (11000/9)*1.2*0.9 = 1320

So the shopkeeper is spending rupees 1000 to buy the dal and is selling the same quantity of dal at rupees 1320. Therefore, profit percentage is (320/1000)*100 = 32%

Considering the data given, Rohan, Sohan, and Rahul are sitting in the shape of an equilateral triangle with sides 3m each. 

Since Priya's distance from Sohan is half her distance from Rahul, she is sitting at a distance of 1 m from Sohan.

Draw a perpendicular AD on BC.

In $$\triangle$$ ADC, using the Pythagoras theorem,

$$AC^2=AD^2+DC^2$$

$$3^2=AD^2+1.5^2$$

$$AD=\frac{3\sqrt 3}{2}$$

In $$\triangle ADE, using the Pythagoras theorem,

$$AE^2=AD^2+DE^2$$

$$AE^2=\frac{27}{4}+\frac{1}{4}=7$$

$$AE=\sqrt 7$$

Hence, the answer is option C.

No of persons who drink coke = 2x + 57/x

As the no. of persons who drink coke will be an integer so 57/x must be an integer so x can be 1, 3, 19 or 57.

No. of persons who drink neither fruit juice nor coke = 57/3x = 19/x this also should be an integer, so x= 1 or 19 only

When x=1, no. of persons who drink coke = 2+57 = 59

When x=19, no. of persons who drink coke = 38 + 3 = 41

For both Ishika and Mishika to agree on a statement either both have to speak the truth or both have to speak false.

Probability of both speaking truth = (60/100)*(85/100) = 204/400

Probability of both speaking false = (40/100)*(15/100) = 24/400

The probability that the statement is true when Ishika and Mishika both agree on a statement = (204/400)/{(204/400)+(24/400)} = 204/228 = 51/57

From the 5th term onwards the last two of all the terms will 00.

The last two digits of 24 to the power of an even number will be 76 always.

So, last two digits of the above expression will be the last two digits of $$1+2\left(2\right)^2+3\left(6\right)^6+4\left(76\right)$$

=1+8+139968+304= 140281

So last two digits is 81

Let AB and CD be the towers of length 4m and 6m respectively.

Let the length of BF be x therefore, the length of FC will be 10-x.

Triangle BEF is similar to triangle BDC

So, $$\frac{EF}{DC}=\frac{BF}{BC}=\frac{BE}{BD}$$

or, $$\frac{EF}{6}=\frac{x}{10}=\frac{BE}{BD}$$

Therefore, $$EF=\frac{3x}{5}$$

Similarly, triangle EFC is similar to triangle ABC

So, $$\frac{EF}{AB}=\frac{CF}{BC}=\frac{EC}{AC}$$

or, $$\frac{EF}{4}=\frac{10-x}{10}=\frac{EC}{AC}$$

or, $$EF=\ \frac{2\left(10-x\right)}{5}$$

Therefore, $$\frac{2\left(10-x\right)}{5}=\frac{3x}{5}$$

or, $$x=4$$

EF= $$\frac{3x}{5}=2.4\ m$$

$$f\left(y\right)=f\left(f\left(x\right)\right)$$

or, $$f\left(y\right)=f\left(\frac{2x+2}{2x-2}\right)$$

$$f\left(y\right)=\frac{2\left(\frac{2x+2}{2x-2}\right)+2}{2\left(\frac{2x+2}{2x-2}\right)-2}$$

or, $$f\left(y\right)=\frac{8x}{8}=x$$

Therefore x:f(y) = 1:1

Let the speed of the train be x.

Since the train and the bullet are travelling in opposite directions, the relative speed of the train with respect to the bullet = (330 + x) m/s

Now, the distance between the bullets = $$330\times\ 642\ m$$

The train travelled this distance in 10 minutes.

Thus, $$\left(330+x\right)\times\ 600\ =\ 330\times\ 642$$

$$x\times\ 600\ =\ 330\times\ 42$$

Speed of train = 13860/600 = 23.1 m/s

Thus, the correct option is C.

Let the length, breadth and height of the cubhoid be l, b and h respectively.

Therefore of adjacent faces will be lb, bh and hl.

If lb= p, then bh= q and hl=r.

Volume (V) = lbh

$$V^2=\left(lbh\right)^2$$

or, $$V^2=pqr$$