Coach Rahul sat with the score cards of Indian players from the 3 games in a one-day cricket tournament where the same set of players played for India and all the major batsmen got out. Rahul summarized the batting performance through three diagrams, one for each game. In each diagram the three outer triangles communicate the number of runs scored by the three top scorers from India, where K, R, S, V and Y represent Krunal, Rohit, Sanjay, Virat and Yogesh respectively. The Middle triangle in each diagram denotes the percentage of total score that was scored by the top three Indian scorers in that game. No two players score the same number of runs in the same game. Rahul also calculated two batting indices for each player based on his scores in the tournament; the R-index of a batsman is the difference between his highest and lowest scores in the 3 games while the M-index is the middle number, if his scores are arranged in a non-increasing order.
Which of the players had the best M-index from the tournament?
Runs scored by R (r1) and S (s1), r1, s1
< 28 and r1+ +s1? 22
Consider the game against South Africa (G2).
Runs scored by K, R and S = 51 + 49 + 75 = 175
Total runs scored = 175/0.7 = 250
Runs scored by Y (y2) and V (v2), y2, v2
< 49 and y2 + v2? 75
Consider the game against Australia (G3).
Runs scored by R, Y and S = 87 + 55 + 50 = 192
Total runs scored = 192/0.8 = 240
Runs scored by V (v3) and K (k3), v3, k3
< 50, v3+ k3? 48
R's M-index = 49
S's M-index = 50
V's M-index? 49
Y's M-index is either 40 or between 41 and 49.
S had the best M-index.
Hence, o
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(a)
Consider game against Pakistan (G1).
Runs scored by Y, V and K = 40 + 130 + 28 = 198
Total runs scored = 198/0.9 = 220
Runs scored by R (r1) and S (s1), r1, s1
< 28 and r1+ +s1? 22
Consider the game against South Africa (G2).
Runs scored by K, R and S = 51 + 49 + 75 = 175
Total runs scored = 175/0.7 = 250
Runs scored by Y (y2) and V (v2), y2, v2
< 49 and y2 + v2? 75
Consider the game against Australia (G3).
Runs scored by R, Y and S = 87 + 55 + 50 = 192
Total runs scored = 192/0.8 = 240
Runs scored by V (v3) and K (k3), v3, k3
< 50, v3+ k3? 48
R's M-index = 49
S's M-index = 50
V's M-index? 49
Y's M-index is either 40 or between 41 and 49.
S had the best M-index.
Hence, option (b)
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<p> (a)</p><p>Consider game against Pakistan (G1).</p><p>Runs scored by Y, V and K = 40 + 130 + 28 = 198</p><p>Total runs scored = 198/0.9 = 220</p><p>Runs scored by R (r<sub>1</sub>) and S (s<sub>1</sub>), r<sub>1</sub>, s<sub>1</sub> < 28 and r<sub>1</sub>+ +s<sub>1</sub>? 22</p><p>Consider the game against South Africa (G2).</p><p>Runs scored by K, R and S = 51 + 49 + 75 = 175</p><p>Total runs scored = 175/0.7 = 250</p><p>Runs scored by Y (y<sub>2</sub>) and V (v<sub>2</sub>), y<sub>2</sub>, v<sub>2</sub> < 49 and y<sub>2</sub> + v<sub>2</sub>? 75</p><p>Consider the game against Australia (G3).</p><p>Runs scored by R, Y and S = 87 + 55 + 50 = 192</p><p>Total runs scored = 192/0.8 = 240</p><p>Runs scored by V (v<sub>3</sub>) and K (k<sub>3</sub>), v<sub>3</sub>, k<sub>3</sub> < 50, v<sub>3</sub>+ k<sub>3</sub>? 48</p><p>R's M-index = 49</p><p>S's M-index = 50</p><p>V's M-index? 49</p><p>Y's M-index is either 40 or between 41 and 49.</p><p>S had the best M-index.</p><p>Hence, option (b)</p>
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