If students who do not participate in both Chess and Carrom from A is increased by \(\frac{300}{17}\)%, then the number of students participating in Chess from A is decreased by what percent? (Ratio of students participating in Chess to Carrom remains same for A)

Given:

n(A) = 420

Concept used: 

n(A ⋃ B) = n(A) + n(B) - n(A ⋂ B)

Calculation:

Number of past Chess participants,

⇒ 420 = 4m + 3m + 119

⇒ 7m = 301

⇒ m = 43

⇒ Number of past Chess participants = 4m = 172

Non-participants in Class A = 119

If students who do not participate in both Chess and Carrom from A is increased by \(\frac{300}{17}\)%,

⇒ \(\dfrac{300}{17}\)% of 119 = \(\dfrac{3}{17}\) × 119 = 21

Updated number of non participants = 119 + 21 = 140 students

⇒ Number of updated participants,

⇒ 4m + 3m = 420 - 140

⇒ 7m = 280

⇒ m = 40

⇒ Number of updated Chess participants = 4 × 40 = 160 students

Difference = 172 - 160 = 12

⇒ Required ratio = \(\dfrac{12}{172} × 100\) = \(\dfrac{300}{43}\)%

∴ The number of students participating in Chess from Class A is decreased by \(\dfrac{300}{43}\)%.