Difference between number of players who played in all three trophies and number of players who played in both leagues is:

Explanation

3 Detailed solution: Let total number of players be 100x Number of players who had played at both levels = 0.10 × 100x = 10x Number of players who played only at national level = (90x + 250)/2 = 45x + 125 Number of players who played only at international level = 45x – 125 Number of players who played only in Ranji = 0.24 (45x + 125) So, 0.24(45x + 125) = 144/0.48 = 300 So, x = 25 Total number of players = 100x = 100 × 25 = 2500 Number of players who had played at both levels = 10x = 10 × 25 = 250 Number of players who played only at national level = 45x + 125 = 45 × 25 + 125 = 1250 Number of players who played only at international level = 45x - 125 = 45 × 25 - 125 = 1000 Number of players who played only in Ranji = 300 Number of players who played only in CPL = 300 + 200 = 500 So, p + 10 = 500/2500 x 100 = 20 So, p = 10 Let number of players who played only in BBL = 25y So, number of players who played in both Ranji and Irani but not Duleep = (10 + 3) x y = 13y Number of players who played in Irani trophy = 1250 - 630 = 620 Number of players who played only in Irani trophy = (2p - 0.8)% of 1250 = 0.192 × 1250 = 240 Number of players who played in both Ranji and Duleep trophy = (2p + 1.6)% of (1250 + 250) = 0.216 × 1500 = 324 Number of players who played in both Ranji and Duleep trophy but not Irani trophy = 324 - 144 = 180 Number of players who played in both Irani and Duleep trophy but not Ranji trophy = 180/2.25 = 80 So, 13y + 144 + 80 + 240 = 620 Or, 13y = 156 So, number of players who played in both Ranji and Irani but not Duleep = 13y = 156 Also, y = 156/13 = 12 So, number of players who played only in BBL = 25y = 25 × 12 = 300 Number of players who played in both BBL and CPL = 1000 - 300 - 500 = 200 Number of people who played in BBL = 300 + 200 = 500 Number of players who played only in Duleep trophy = 630 – 180 – 300 = 150 National International 1250 25 1000 0 Ranji 180 Duleep 150 BBL 300 144 80 156 300 240 Desired difference = 200 – 144 = 56 = 3p2 – 25p + 6