Q. 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?

Explanation : 

Let N = total runs scored by Team X (in 20 overs).
Team Y ties this score in “10% less overs” than 20, i.e. in 20 – 0.1·20 = 18 overs.

1. Team Y’s actual run rate r = N runs ÷ 18 overs = N/18.
2. If Team Y’s run rate were 50% higher, it would be
r′ = r + 0.5·r = 1.5·r = 1.5·(N/18) = N/12.
3. At this higher rate r′, the overs needed to score N runs would be
N runs ÷ (N/12 runs per over) = 12 overs.

This matches the statement, but it imposes no restriction on N (it cancels out). Any positive N satisfies the conditions.

Therefore, the value of N cannot be determined from the information given.