The average number of students studying Engineering, Commerce and Arts in 2019 is what percentage less than the average number of students studying Management, Computer Science and Science in 2021? (Nearest to an integer)

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

Average number of students studying Engineering, Commerce and Arts in 2019 = $$\ \dfrac{300+225+150}{3}=225$$

Average number of students studying Management, Computer Science and Science in 2021 = $$\ \dfrac{360+324+270}{3}=318$$

Difference in the number of students = 318 - 225 = 93

Percentage difference = $$\ \dfrac{93}{318}\times100=29.24\%$$

Hence, the average number of students studying Engineering, Commerce and Arts in 2019 is 29.24% less than the the average number of students studying Management, Computer Science and Science in 2021. 

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