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 find the number of runs scored by Australia, let's first solve the problem step by step:

Step 1: Calculate the number of overs India played when they tied the scores.
Since India tied the scores in 20% less overs than Australia, we need to find 20% of 50 overs.
20% of 50 overs = (20/100) * 50 = 10 overs

So, India tied the scores in 50 - 10 = 40 overs.

Step 2: Calculate the total number of overs in which India would have tied the scores if their run rate was 33.33% higher.
Since India would have tied the scores 10 overs earlier, we need to find 10 overs less than the 40 overs they played.
10 overs less than 40 overs = 40 - 10 = 30 overs

Step 3: Calculate the percentage increase in India's run rate.
To find the percentage increase, we need to calculate 33.33% of India's average run rate.
33.33% of the average run rate = (33.33/100) * average run rate = 0.3333 * average run rate

Step 4: Calculate India's average run rate after the 33.33% increase.
India's average run rate after the increase = average run rate + 0.3333 * average run rate
= 1.3333 * average run rate

Step 5: Calculate the number of runs India would have scored if their run rate was 33.33% higher.
To find the runs scored by India, we need to multiply their average run rate after the increase by the number of overs.
Runs scored by India = (1.3333 * average run rate) * 30 overs

Step 6: Equate the runs scored by Australia to the runs scored by India.
Since both teams tied the scores, we can set up the following equation:
X = (1.3333 * average run rate) * 30 overs

Step 7: Solve for X (the runs scored by Australia).
Divide both sides of the equation by (1.3333 * 30) to isolate X:
X = [(1.3333 * average run rate) * 30 overs] / (1.3333 * 30)

The 30 overs and 1.3333 * 30 cancel out, leaving us with:
X = average run rate

Therefore, the number of runs scored by Australia is equal to their average run rate.