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