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?

The correct option is Cannot be determined.

Let us analyze the given information step-by-step to understand why the exact number of runs cannot be determined.

Step 1: Understand the overs bowled for Team Y
Team X scored a total of $N$ runs in 20 overs.
Team Y tied the score (i.e., scored $N$ runs) in 10% less overs than Team X.
Number of overs taken by Team Y = 20 - (10% of 20) = 20 - 2 = 18 overs.

Step 2: Express Team Y's average run rate
Team Y's initial run rate, $R_1$, is the total runs divided by the number of overs:

$R_1=\frac{N}{18}$

Step 3: Analyze the condition with a 50% higher run rate
If Team Y’s run rate were 50% higher, the new run rate $R_2$ would be:

$R_2=1.5\times R_1=1.5\times \frac{N}{18}=\frac{N}{12}$

Step 4: Check the overs required to tie the score with the higher run rate
With the new run rate $R_2$, the time/overs required to reach total runs $N$ is:

$\text{Overs}=\frac{N}{R_2}=\frac{N}{N/12}=12\text{overs}$

Conclusion:
The given condition that "the scores would have been tied in 12 overs" is an identity that holds true for any value of $N$. The variable $N$ cancels out completely from both sides of the equation.
Since no independent equation or specific numerical constraint is available to solve for $N$, the total runs scored by Team X cannot be uniquely determined.