The ratio of males and females students studying Computer Science in 2019 is 3 : 4 and it is 7 : 5 for the students studying Management in the same year. 30% of the students studying Management in 2021 are females. The number of male students studying Management in 2021 is what percentage less than the total number of female students studying Computer Science and Management in 2019?

The required figure is given below:

Let the total number of students in 2019 be $$x$$.

Number of Commerce students = $$15\%\ of\ x=225$$ (given)

$$x=1500$$

Number of students in 2021 increased by 20% as compared to 2019.

Total number of students in 2021 = $$1500\times\left(1+20\%\right)=1800$$

In 2019,

Number of students in Computer Science = 21% of 1500 = 315

Number of students in Arts = 10% of 1500 = 150

Number of students in Science = 18% of 1500 = 270

Number of students in Engineering = 20% of 1500 = 300

Number of students in Management = 16% of 1500 = 240

Number of students in Commerce = 225 (given)

In 2021,

Number of students in Computer Science = 18% of 1800 = 324

Number of students in Arts = 12% of 1800 = 216

Number of students in Science = 15% of 1800 = 270

Number of students in Engineering = 25% of 1800 = 450

Number of students in Management = 20% of 1800 = 360

Number of students in Commerce = 10% of 1800 = 180

Let the number of male and female students in Computer Science in 2019 be $$3x$$ and $$4x$$ respectively. 

Total number of students in Computer Science in 2019 = $$3x+4x=7x$$

Total number of students in Computer Science in 2019 = 315 (given)

$$7x=315$$

$$x=45$$

Number of male students in Computer Science in 2019 = $$\left(3\times x\right)=\left(3\times45\right)=135$$

Number of female students in Computer Science in 2019 = $$\left(4\times x\right)=\left(4\times45\right)=180$$

Let the number of male and female students in Management in 2019 be $$7x$$ and $$5x$$ respectively.

Total number of students in Management in 2019 = $$7x+5x=12x$$

Total number of students in Management in 2019 = 240 (given)

$$12x=240$$

$$x=20$$

Number of male students in Management in 2019 = $$\left(7\times x\right)=\left(7\times20\right)=140$$

Number of female students in Management in 2019 = $$\left(5\times x\right)=\left(5\times20\right)=100$$

Total number of students in Management in 2021 = 360

Number of female students = 30% of 360 = 108

Number of male students = 360 - 108 = 252

Number of male students in Management in 2021 = 252

Total number of female students in Computer Science and Management in 2019 = (180 + 100) = 280

Difference = 280 - 252 = 28 

Percentage = $$\ \dfrac{28}{280}\times100\ =\ 10\%$$

Hence, the number of male students in Management in 2021 is 10% less than the total number of female students in Computer Science and Management is 2019. 

$$\therefore\ $$ The required answer is C.