CMAT 2019 Question Paper

Given Speed of surya = 25 km/hr = $$25\times \frac{5}{18} = \frac{125}{18}$$ m/s.

Time taken(T) = Distance Travelled/ Speed

$$\Rightarrow T =\frac{500}{\frac{125}{18}} = 72$$ sec 

Hence the time taken by Mr. Surya is '72 sec' or '1.2 min'. 

As per the empirical rule, approximately 99.7% of the data in a bell-shaped distribution lies within three standard deviations of the mean, or $$\mu \pm 3\sigma$$.  $$\mu \pm 6\sigma$$ will have approximately 99.99967% of the data. Hence, option C.

The topper of the class is the one who gets a highest overall score. Let us check the options, who has got the overall score.

Option A:

The overall score of Maya = 90 + 50 + 90 + 60 + 70 + 80 = 440 marks 

Option B:

The overall score of Arya = 100 + 80 + 88 + 60 + 80 + 70 = 478 marks

Option C:

The overall score of Rupesh = 80 + 55 + 85 + 95 + 50 + 90 = 455 marks

Option D:

The overall score of Riya = 90 + 72 + 70 + 72 + 91 + 70 = 465 marks

So, the topper of the class is Arya, with a overall score of 478 marks.

Given, Rajesh can check the quality of 1000 items in 5 hours

$$\Rightarrow$$ Efficiency of Rajesh = 200 items/hr.

Also given, Rakesh can complete the 75% of same job in 3 hours

$$\Rightarrow$$ time taken by Rakesh to complete 100% of the job = $$\frac{100}{75}\times 3$$ = 4 hours.

$$\Rightarrow$$ Efficiency of Rakesh = 250 items/hr.

Given in the process of checking 1300 items, Rakesh spends only 2 hours. Let say time spent by Rajesh be 't' hours, which is also the total time taken.

Total Work = Efficiency $$\times$$ time taken 

$$\Rightarrow 1300 = 250\times 2 + 200\times t$$

$$\Rightarrow 200t = 800$$

$$\Rightarrow t = 4$$

Hence the time taken in the process of checking 1300 items is 4 hours.

Let the cost of each orange, banana and apple be Rs. 'o' , 'b' , and 'a' respectively.

Given, Two oranges, three bananas and four apples cost Rs. 15

$$\Rightarrow$$ 2o + 3b + 4a = 15..........(1)

Also given, Three oranges, two bananas and one apple cost Rs. 10

$$\Rightarrow$$ 3o + 2b + a = 10............(2)

Adding (1) and (2), we get,

5o + 5b + 5a = 25

$$\Rightarrow$$ o + b + a = 5

Then the cost of three oranges, three bananas and three apples is given as

3o + 3b + 3a = 3 [o + b + a] = 3$$\times$$ 5 = Rs. 15 

$$360\sqrt?$$ + 4500 = 19700 - 9800

$$\Rightarrow 360\sqrt? + 4500 = 9900$$

$$\Rightarrow 360\sqrt? = 5400$$

$$\Rightarrow \sqrt? = 15$$

$$\Rightarrow ? = 15^2$$

$$\Rightarrow ? = 225$$

Curved surface area of cylindrical pillar is given as A = 2$$\pi$$rh, where 'r' is base radius and 'h' is height of the cylinder.

So curved surface area of each pillar A = $$2\times \pi\times 0.35\times 5 = 11 m^2$$

Given there are 30 cylindrical pillars.

The curved surface area of half the number of pillars = 15 * A = 165 $$m^2$$.

Given rate of painting is Rs. 10 per $$m^2$$

The cost of painting curved surface of half the number of pillars = Curved surface area * rate of painting

= $$165\times 10$$

= Rs. 1650. 

Probability = Expected number of outcomes/ Total number of outcomes.

Total number of outcomes =  The number of ways of selecting 3 professors at random from a total of 10 professors.

= 10C3 = 120 ways.

Expected number of outcomes = Selecting 3 professors so that at least one of the junior professor is selected.

The possible cases are,

Case(1): Selecting 1 junior professor out of 4 and Selecting 2 senior professor out of 6 = 4C1 * 6C2.

Case(2): Selecting 2 junior professor out of 4 and Selecting 1 senior professor out of 6 = 4C2 * 6C1.

Case (3): Selecting 3 junior professor out of 4  = 4C3.

So Expected number of outcomes = 4C1 * 6C2 + 4C2 * 6C1 + 4C3 = $$4\times 15 + 6\times 6 + 4$$ = 100 ways.

Probability = $$\frac{100}{120} = \frac{5}{6}$$ 

In a clock, 

In one revolution the minute hand covers 60°

$$\Rightarrow$$ 60 minutes = 360°

$$\Rightarrow$$ 1 minute = 6°.

$$\Rightarrow$$ for every minute the minute hand covers 6°.

Similarly In one revolution the hour hand covers 12 hours.

$$\Rightarrow$$ 12 hours = 360°

$$\Rightarrow$$ 1 hour = 30°.

$$\Rightarrow$$ for every hour, the hour hand covers 30°.

So at 5.20 P.M. the hour hand must have covered 5 * 30° = 150° + 20*1/2 = 160

and minute hand must have covered 20 * 6° = 120°.

So the angle created by two hands of the clock when the time is 5.20 P.M. = 160 - 120 = 40°.

Given, Total volume of soaps sold = 680 lakh units.

Volume of Lux sold = 136 lakh units.

$$\Rightarrow$$ Percentage of Lux sold = $$\frac{136}{680}\times 100$$ = 20% 

Also given,

percentage of Lifebuoy sold is 30%,

 percentage of Camay 10%,

 percentage of Liril 15% and 

percentage of Mysore Sandal 10% 

From the pie chart

The percentage of Lux + Lifeboy + Camay + Liril + Mysore Sandal + Others  sold = 100%

$$\Rightarrow$$ The market share of others = 100 - 20 - 30 - 10 - 15 - 10 = 15%