The number of students learning Carrom in college C is ________ % less than the number of students learning Chess in college A. 

Let's solve the set by creating a table:

For College A:

Number of chess players + number of squash players = 2100 .....(1)

Number of chess players - number of squash players = 300    .....(2)

Solving equations (1) and (2):

Number of chess players = 1200

number of squash players = 900

Now, for Number of carrom players, since 70% of the total students = 2100,

hence, total students = \(\frac{2100×100}{70}= 3000\).

Number of carrom players = 900.

Similarly, For College B:

Number of chess players + number of squash players = 1170 .....(3)

Number of chess players - number of squash players = 30    .....(4)

Solving equations (3) and (4):

Number of chess players = 600

number of squash players =570

Now, for Number of carrom players, since 65% of the total students = 1170,

hence, total students = \(\frac{1170×100}{65}= 1800\).

Number of carrom players = 630.

Similarly, For College C:

Number of chess players + number of squash players = 1260 .....(5)

Number of chess players - number of squash players = 140    .....(6)

Solving equations (5) and (6):

Number of chess players = 700

number of squash players = 560

Now, for Number of carrom players, since 60% of the total students = 1260,

hence, total students = \(\frac{1260×100}{60}= 2100\).

Number of carrom players = 840.

Similarly, For College D:

Number of chess players + number of squash players = 1800 .....(7)

Number of chess players - number of squash players = 400    .....(8)

Solving equations (7) and (8):

Number of chess players = 1100

number of squash players = 700

Now, for Number of carrom players, since 75% of the total students = 1800,

hence, total students = \(\frac{1800×100}{75}= 2400\).

Number of carrom players = 600.

Required percentage = [(1200 - 840) / 1200] × 100

⇒ 360/1200 × 100

⇒ 360/12 = 30%

Hence, the correct answer is option (4).