Question: In the first One-day International Cricket match between India and England at Lords, the bowling honours in the Indian team was shared by Kapil Dev, Madanlal and Binni.
1. Either Kapil took half the wickets or one of the players was run out.
2. Either Kapil took 5 wickets and Binni took 3 or Madanlal took one more than Binni.
3. The sum of Kapil's victims and twice of Madanlal's victims is one more than three times Binni's victims.
Can you tell the number of wickets each of them took?
Answer:
Statement (3) can be represented as K + 2M = 3B + 1
where,
K - wickets taken by Kapil Dev
M - wickets taken by Madanlal
B - wickets taken by Binni
Let's consider statement (2). If Kapil took 5 wickets and Binni took 3 wickets, then from equation above, Madanlal should have taken two-and-a-half wickets which is impossible. Hence, Madanlal took one more than Binni i.e. M = B + 1
Substitute M = B + 1 in first equation,
K + 2M = 3B + 1
K + 2(B + 1) = 3B + 1
K + 2B + 2 = 3B + 1
K = B - 1
Now consider statement (1). If Kapil took half the wickets i.e. 5 wickets, Binni should have taken 6 wickets and Madanlal should have taken 7 wickets. But this is impossible as there are just 10 wickets. Hence, one player was run out and total wickets taken by them must be 9.
K + M + B = 9
(B - 1) + (B + 1) + B = 9
B = 3 wickets.
Hence, wickets taken by Kapil, Madanlal and Binni are 2, 4 and 3 respectively.
There are 2 more possible answers as total number of wickets fallen is not specified. In the above answer, we assumed maximum wickets i.e. 10.
* 10 wickets : Kapil=2, Madanlal=4, Binni=3, Runout=1
* 7 wickets : Kapil=1, Madanlal=3, Binni=2, Runout=1
* 4 wickets : Kapil=0, Madanlal=2, Binni=1, Runout=1