Team X scored a total of N runs in 20 overs. Team Y tied the score in 10% less overs. Had Team Y's average run rate (runs per over) been 50% higher, the scores would have been tied in 12 overs. How many runs were scored by Team X?

Correct Option

Let N represent the total runs scored by Team X. Team X scored N runs in 20 overs.

Team Y tied the score, meaning Team Y also scored N runs. Team Y completed this in 10% fewer overs than Team X.

• Overs taken by Team Y = 20 - (0.10 * 20) = 20 - 2 = 18 overs.
• Team Y's actual average run rate = N runs / 18 overs = N/18 runs per over.

The problem states that if Team Y's average run rate had been 50% higher, the scores would have been tied in 12 overs.

• Hypothetical higher run rate for Team Y = (N/18) * (1 + 0.50) = (N/18) * (1.5) = (N/18) * (3/2) = N/12 runs per over.
• If Team Y scored N runs at this hypothetical rate in 12 overs, the total runs would be: (N/12) * 12 = N runs.

This calculation results in the identity N = N. This indicates that the given conditions are consistent with each other but do not provide sufficient information to determine a unique numerical value for N. Therefore, the exact number of runs scored by Team X cannot be determined from the provided data.

Incorrect Options

Options 1 (72), 2 (144), and 3 (216) are incorrect because the problem's conditions lead to an indeterminate equation (N=N). This implies that while the scenario is mathematically consistent, there is no unique solution for N based on the given information. Any specific numerical value for N, such as 72, 144, or 216, cannot be derived or confirmed from the problem's constraints.