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…
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?
72
144
216
Cannot be determined
Solution
Team Y ties N runs in 10% less overs = 18 overs, so Y's run rate = $\dfrac{N}{18}$. With a 50% higher run rate $\dfrac{N}{18}\times\dfrac{3}{2} = \dfrac{N}{12}$, the runs in 12 overs = $\dfrac{N}{12}\times 12 = N$. This holds for every value of N - the data is consistent for any N, giving no unique value. Hence X's score cannot be determined.