In a school there are three batches of players who play cricket, football and hockey. An incomplete chart of number of students playing an individual sport belonging to an individual batch is displayed in the following table :
| Batch I | Batch II | Batch III | Total | |
|---|---|---|---|---|
| Cricket players | 8 | 14 | ||
| Football players | 10 | 16 | ||
| Hockey players | 6 | 6 | 17 | |
| Total |
Which one of the following is correct ?
– Cricket: Batch I + Batch II + 8 = 14 => Batch I + Batch II = 6
– Football: Batch I + Batch II + 10 = 16 => Batch I + Batch II = 6
– Hockey: 6 + Batch II + 6 = 17 => Batch II = 17 – 12 = 5
Using Batch II = 5 in the first two equations:
– Batch I + 5 = 6 => Batch I = 1
– Batch I + 5 = 6 => Batch I = 1 (Consistent)
The number of students in each batch is the sum of players across sports:
– Batch I Total: Cricket (1) + Football (1) + Hockey (6) = 8
– Batch II Total: Cricket (5) + Football (5) + Hockey (5) = 15
– Batch III Total: Cricket (8) + Football (10) + Hockey (6) = 24
– Grand Total: 8 + 15 + 24 = 47 (Also 14 + 16 + 17 = 47)
Now, evaluate the options:
A) Batch II is empty (Batch II has 15 students) – False
B) Batch I and Batch II do not have equal number of students (Batch I = 8, Batch II = 15. 8 != 15) – True
C) Batch I and Batch III can have equal number of students (Batch I = 8, Batch III = 24. They are not equal) – False
D) Batch II and Batch III can have equal number of students (Batch II = 15, Batch III = 24. They are not equal) – False
| Batch I | Batch II | Batch III | Total | |
|---|---|---|---|---|
| Cricket players | 1 | 5 | 8 | 14 |
| Football players | 1 | 5 | 10 | 16 |
| Hockey players | 6 | 5 | 6 | 17 |
| Total | 8 | 15 | 24 | 47 |