Question:
Team A is a cricket team picking its playing eleven from its regular pool of batsmen for a league where it faces Teams B, C and D. The table below lists the past performance record of Team A's top 10 batsmen: their career batting average, and three tendencies expressed as a percentage of their innings, namely how often they get out for under 20 runs, how often they get out for a score close to their own average, and how often they go on to score more than a century.
For reference, the average score of the top 5 batsmen of each opposing team is: Team C, 270 runs; Team B, 215 runs; Team D, 180 runs; Team A (itself), 215 runs.
Team A is playing its first match with team C. Based on the statistics above, whom should the manager choose so that the team has maximum chances of winning?
Team A is a cricket team picking its playing eleven from its regular pool of batsmen for a league where it faces Teams B, C and D. The table below lists the past performance record of Team A's top 10 batsmen: their career batting average, and three tendencies expressed as a percentage of their innings, namely how often they get out for under 20 runs, how often they get out for a score close to their own average, and how often they go on to score more than a century.
For reference, the average score of the top 5 batsmen of each opposing team is: Team C, 270 runs; Team B, 215 runs; Team D, 180 runs; Team A (itself), 215 runs.
Team A is playing its first match with team C. Based on the statistics above, whom should the manager choose so that the team has maximum chances of winning?
For reference, the average score of the top 5 batsmen of each opposing team is: Team C, 270 runs; Team B, 215 runs; Team D, 180 runs; Team A (itself), 215 runs.
Team A is playing its first match with team C. Based on the statistics above, whom should the manager choose so that the team has maximum chances of winning?
Show Hint
Total the career averages of each five-man group first, since Team C's own batsmen average 270 and demand Team A's strongest possible line-up.
Updated On: Jul 10, 2026
- RD, ST, SG, MD, YS
- VS, YS, RU, MD, MT
- RD, ST, SG, VS, MD
- YS, RU, VS, MK, MD
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
This is the first match of the league, against Team C, whose top 5 batsmen average 270 runs, the highest of any opposing team. So Team A needs its strongest possible batting group for this match. We must again pick the 5 of the 10 listed batsmen that gives A the best chance of winning.
Step 2: Key Formula or Approach:
As before, add up each option's 5 batsmen's career averages to estimate expected runs, then check the average percentage dismissed below 20 to estimate how risky the line-up is. The group with the highest combined average and the lowest combined failure rate is the safest pick against a strong opponent like C.
Step 3: Detailed Explanation:
Recall the averages: RD 40, ST 44, SG 41, VS 31, RU 28, YS 35, VV 35, MK 30, MT 36, MD 45. Add up the average of each option's 5 batsmen:
Option A, RD + ST + SG + MD + YS: \(40+44+41+45+35=205\)
Option B, VS + YS + RU + MD + MT: \(31+35+28+45+36=175\)
Option C, RD + ST + SG + VS + MD: \(40+44+41+31+45=201\)
Option D, YS + RU + VS + MK + MD: \(35+28+31+30+45=169\)
Option E, ST + VS + RU + MD + SG: \(44+31+28+45+41=189\)
Option A has the highest combined average, 205 runs, just ahead of C at 201, and well ahead of E, B and D, all below 190. Options B and D both include RU, whose average of 28 is the lowest of the ten batsmen, so they cannot be Team A's strongest possible group.
Between A and C, check the failure rate. For A: RD 20, ST 20, SG 25, MD 30, YS 40, which averages to \(\frac{20+20+25+30+40}{5}=27\%\). For C: RD 20, ST 20, SG 25, VS 50, MD 30, which averages to \(\frac{20+20+25+50+30}{5}=29\%\). A is both slightly stronger on average and slightly safer than C, since C swaps YS (average 35, only 40 percent risk of falling under 20) for VS, who is dismissed below 20 in half of his innings. So A edges out C on both measures.
Step 4: Final Answer:
Option A, RD, ST, SG, MD, YS, has the highest total career average (205) and a lower failure rate than its closest rival C, so it gives Team A the best chance of winning its opening match against the strong Team C line-up. As with the earlier question in this caselet, the official XAT key marks this question's data as ambiguous with no fixed correct option; the calculation above identifies the strongest supported choice.
\[ \boxed{\text{Option 1: RD, ST, SG, MD, YS}} \]
This is the first match of the league, against Team C, whose top 5 batsmen average 270 runs, the highest of any opposing team. So Team A needs its strongest possible batting group for this match. We must again pick the 5 of the 10 listed batsmen that gives A the best chance of winning.
Step 2: Key Formula or Approach:
As before, add up each option's 5 batsmen's career averages to estimate expected runs, then check the average percentage dismissed below 20 to estimate how risky the line-up is. The group with the highest combined average and the lowest combined failure rate is the safest pick against a strong opponent like C.
Step 3: Detailed Explanation:
Recall the averages: RD 40, ST 44, SG 41, VS 31, RU 28, YS 35, VV 35, MK 30, MT 36, MD 45. Add up the average of each option's 5 batsmen:
Option A, RD + ST + SG + MD + YS: \(40+44+41+45+35=205\)
Option B, VS + YS + RU + MD + MT: \(31+35+28+45+36=175\)
Option C, RD + ST + SG + VS + MD: \(40+44+41+31+45=201\)
Option D, YS + RU + VS + MK + MD: \(35+28+31+30+45=169\)
Option E, ST + VS + RU + MD + SG: \(44+31+28+45+41=189\)
Option A has the highest combined average, 205 runs, just ahead of C at 201, and well ahead of E, B and D, all below 190. Options B and D both include RU, whose average of 28 is the lowest of the ten batsmen, so they cannot be Team A's strongest possible group.
Between A and C, check the failure rate. For A: RD 20, ST 20, SG 25, MD 30, YS 40, which averages to \(\frac{20+20+25+30+40}{5}=27\%\). For C: RD 20, ST 20, SG 25, VS 50, MD 30, which averages to \(\frac{20+20+25+50+30}{5}=29\%\). A is both slightly stronger on average and slightly safer than C, since C swaps YS (average 35, only 40 percent risk of falling under 20) for VS, who is dismissed below 20 in half of his innings. So A edges out C on both measures.
Step 4: Final Answer:
Option A, RD, ST, SG, MD, YS, has the highest total career average (205) and a lower failure rate than its closest rival C, so it gives Team A the best chance of winning its opening match against the strong Team C line-up. As with the earlier question in this caselet, the official XAT key marks this question's data as ambiguous with no fixed correct option; the calculation above identifies the strongest supported choice.
\[ \boxed{\text{Option 1: RD, ST, SG, MD, YS}} \]
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