A team of 5 players Arpit, Bimal, Chatur, Dinu and Elan participated in a ‘Freaket’ tournament and played four matches (1 to 4). The following table gives partial information about their individual scores and the total runs scored by the team in each match.

Each column has two values missing. These are the runs scored by the two lowest scorers in that match.None of the two missing values is more than 10% of the total runs scored in that match.

Match-1 | Match-2 | Match-3 | Match-4 | ||

Runs scored by player | Arpit | 100 | 53 | ||

Bimal | 88 | 65 | 52 | ||

Chatur | 110 | ||||

Dinu | 72 | 75 | 20 | 56 | |

Elan | 60 | 78 | |||

Total | 270 | 300 | 240 | 200 |

**Q1. **What is the maximum possible percentage contribution of Arpit in the total runs scored in the four matches?

- 19.7%
- 19.9%
- 20.1%
- 20.2%

**Q2. **If the absolute difference between the total runs scored by Arpit and Chatur in the four matches is minimum possible then what is the absolute difference between total runs scored by Bimal and Elan in the four matches?

- 32
- 37
- 27
- Cannot be determined

**Q3. **The players are ranked 1 to 5 on the basis of the total runs scored by them in the four matches, with the highest scorer getting Rank 1. If it is known that no two players scored the same number of total runs, how many players are there whose rank can be exactly determined?

- 0
- 1
- 3
- 5

Let us analyse the scores of Match-1 first:

Runs scored by Bimal, Dinu and Elan = 88 + 72 + 60 = 220

Hence, runs scored by Arpit and Chatur = 270 – 220 = 50

Also 10% of 270 = 27

So, both Arpit and Chatur can score a maximum of 27 runs but the sum of their scores should be 50.

Arpit’s score’s range in Match-1 is 23–27 and subsequently Chatur’s score’s range in Match-1 is 27–23.

Similarly Chatur and Dinu scored 30 runs each in Match-2.

In Match-3 even though 10% of 240 = 24, as Dinu scored 20 runs, both Arpit and Bimal can score a maximum of 19 runs, but the sum of their scores should be 32.

In Match-4, Chatur and Elan combined scored 200 – 53 – 52 – 56 = 39 runs. As 10% of 200 = 20, one of Chatur or Elan scores 20 runs and the other scores 19 runs.

The table can be re-written as :

Match-1 | Match-2 | Match-3 | Match-4 | ||

Runs scored by player | Arpit | 27–23 | 100 | 19–13 | 53 |

Bimal | 88 | 65 | 13–19 | 52 | |

Chatur | 23–27 | 30 | 110 | 19–20 | |

Dinu | 72 | 75 | 20 | 56 | |

Elan | 60 | 30 | 78 | 20–19 | |

Total | 270 | 300 | 240 | 200 |

**Q1. **Maximum possible runs scored by Arpit in Match-1 = 27

Maximum possible runs scored by Arpit in Match-3 = 19

Maximum possible percentage contribution:

(27+100+19+53)/(270+300+240+200)x100% = 199/1010x100%

= 19.7%

**Q2. **Maximum possible total runs scored by Chatur in the four matches = 27 + 30 + 110 + 20 = 187.

In such a case minimum possible total runs scored by Arpit in the four matches = 23 + 100 + 13 + 53 = 189.

Difference = 189 – 187 = 2 (minimum possible) Subsequently total runs scored by Bimal in the four matches = 88 + 65 + 19 + 52 = 224.

Also, total runs scored by Elan in the four matches = 60 + 30 + 78 + 19 = 187

Absolute difference = 224 – 187 = 37

**Q3. **Individual ranges for total score:

Arpit-> 189-199

Bimal-> 218-224

Chatur-> 182-187

Dinu-> 223

Elan-> 187-188

Least total will be of Chatur (Rank 5)

2nd least will be Elan (Rank 4)

Rank 3 must be of Arpit.

It is not possible to determine the exact ranks of Bimal and Dinu.

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