CMAT 2022

Let the number of boys be 4x and number of girls be 6x

Given, 4x+6x = 50

                   x = 5

Number of boys = 20 and number of girls = 30

Average marks of girls = 60

Total marks scored by girls = 60$$\times\ $$30 = 1800

Average marks score by batch = 62

Total marks scored by batch = 62$$\times\ $$50 = 3100

Marks scored by boys = 3100 - 1800 = 1300

Average marks of boys = $$\frac{1300}{20}$$ = 65

Answer is option D.

A : B : C : D = 24($$\frac{3}{12}$$) : 10($$\frac{5}{12}$$) : 35($$\frac{4}{12}$$) : 21($$\frac{3}{12}$$)

A : B : C ; D = 6 : $$\frac{25}{6}$$ : $$\frac{35}{3}$$ : $$\frac{21}{4}$$

A : B: C : D = 72 : 50 : 140 : 63

Anil's rent = $$\frac{72}{72+50+140+63}\times\ $$ Total rent

720 = $$\frac{72}{325}\times\ $$ T

T = Rs 3,250

Answer is option B.

Volume of copper wire melted will be equal to volume of sphere.

Volume of copper wire = Area $$\times\ $$ length = $$\pi\ \left(\frac{2}{10}\right)^2\times\ 24300\ cm^3$$

Let the radius of sphere be r

$$\frac{4}{3}\pi\ r^{3\ \ }=\ \pi\ \left(\frac{2}{10}\right)^2\times\ 24300\ cm^3$$

$$r^3$$ = 729

r = 9 cm

Diameter of sphere = 2(9) = 18 cm

Answer is option B.

Given, cost price is 80% of selling price

C.P = 0.8 S.P

Profit = $$\ \frac{\ S.P\ -\ C.P}{C.P}\times\ 100$$

         = $$\ \frac{\ S.P\ -\ 0.8S.P}{0.8S.P}\times\ 100$$

         =$$\ \frac{0.2}{0.8}\times\ 100$$

         = 25%

Answer is option B

Number of ways of selecting 2 red balls and 1 green ball = $$15_{C_2}.\ 10_{C_1}$$

Number of ways of selecting 3 balls = $$25_{C_3}$$

Probability of selecting 2 red balls and 1 green ball = $$\ \frac{15_{C_2}.10_{C_1}}{25_{C_3}}$$ = $$\frac{21}{46}$$

Answer is option A.

Let us consider with average speed of 40 km/hr, train reached its destination in time t hrs

with average speed of 30 km/hr, it takes t +$$\frac{36}{60}$$ hrs

Distance will be same in both the cases

40t = 30t + 18

10t = 18

t = $$\frac{18}{10}$$

Distance = 40t = 40$$\times\ \frac{18}{10}$$ = 72 km

Answer is option A.

Initial amount = Rs 4000

Compounded amount after one year = $$4000\left(1+\frac{15}{100}\right)=4600$$

Final amount after one year = 4600 - 1500 = Rs 3100

Compounded amount after at the end of two years = $$3100\left(1+\frac{15}{100}\right)=3565$$

Final amount at the end of two years = 3565-1500 = Rs 2065

Compounded amount after at the end of three years = $$2065\left(1+\frac{15}{100}\right)=2374.75$$

Final additional amount at the end of three years = 2374.75-1500 = Rs 874.75

The answer is option D.

Total production = 1500 units

A) A and G production = 240 + 180 = 420 (not greater than 500)

B) B and F production = 165 + 75 = 240 ( is less than 250)

C) C and E production = 315 + 390 = 705 

D) D and G production = 135 +180 = 315 ( not less than 200)

E) E, F and G production = 390 + 75 + 180 = 645 ( not equal to 545)

Only (B) and (C) are true.

Answer is option B.

Total number of votes = 15200

15% of total votes are invalid, this implies 85% are valid.

55% of valid votes are secured by winner, this implies 45% of valid votes are secured by loser

Voted secured by loser = $$\frac{45}{100}\times\ \frac{85}{100}\times\ 15200$$ = 5814

Answer is option C.

It is given that $$\frac{1}{x}$$ is positive and $$\frac{1}{y}$$ is negative, this implies that x is positive and y is negative.

A) $$\frac{1}{x}\ +\ \frac{1}{y}$$ is positive, we know x is positive, and y is negative, but we cannot conclude which value is greater. Therefore, this may or may not be true.

B)$$\frac{1}{x}-\frac{1}{y}$$ is positive; we know that x is positive and y is negative. So this statement is definitely true.

C) $$\ \frac{\ x-y}{xy}$$= -($$\frac{1}{x}-\frac{1}{y}$$)

As $$\frac{1}{x}-\frac{1}{y}$$ is positive, $$\ \frac{\ x-y}{xy}$$ is negative and statement is true.

D) $$\frac{1}{xy}$$ is negative as x is positive and y is negative. Therefore, the statement is false.

E)$$\frac{1}{x^2}-\frac{1}{y^2}$$ is positive only when $$y^2>x^2$$, but we cannot conclude which value is greater. Therefore, this may or may not be true.

Only (B) and (C) are true.

Answer is option B