Ratio of number of players who played in both Ranji and Irani trophy but not in Duleep trophy to number of players who played in both Irani and Duleep trophy but not in Ranji trophy is:

Explanation

4 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 ratio = 156:80 = 39:20