Australia scored a total of X runs in 50 overs. India tied the scores in 20% less overs. If India's average run rate had been 33.33% higher the scores would have been tied 10 overs earlier. Find how many runs were scored by Australia?
To solve this problem, we'll use a system of equations.
Let's assume that Australia scored X runs in 50 overs. This means their run rate is X/50 runs per over.
India tied the scores in 20% less overs, which is 50 - 0.2*50 = 40 overs.
If India's average run rate had been 33.33% higher, their new run rate would be 1.3333 * (X/50) = 4X/150 runs per over.
And if the scores were tied 10 overs earlier, India would have scored the same number of runs in 40 - 10 = 30 overs.
Now we can set up the following equation based on the above information:
(4X/150) * 30 = X
Let's solve this equation to find the value of X (the runs scored by Australia):
First, we'll simplify the equation:
(4X/150) * 30 = X
Now, let's cross multiply:
4X * 30 = 150 * X
120X = 150X
Now, let's subtract 120X from both sides:
0 = 150X - 120X
30X = 0
Divide both sides by 30:
X = 0
Therefore, according to the given information, Australia scored 0 runs.