Q. Passage-2
The history of renewable energy suggests there is a steep learning curve, meaning that, as more is produced, costs fall rapidly because of economies of scale and learning by doing. The firms’ green innovation is path-dependent: the more a firm does, the more it is likely to do in the future. The strongest evidence for this is the collapse in the price of solar energy, which became about 90% cheaper during the 2010s, repeatedly beating forecasts. Moving early and gradually gives economies more time to adjust, allowing them to reap the benefits of path-dependent green investment without much disruption. A late, more chaotic transition is costlier.
Q.9) 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?
Exp) Option d is the correct answer
Given:
- Team X scored N runs in 20 overs.
- Team Y tied the score, i.e., also scored N runs, but did so in 10% fewer overs, which is 18 overs.
- If Team Y’s run rate had been 50% higher, they would have tied the score in 12 overs.
Let Team Y’s actual run rate be denoted by R. Since they scored N runs in 18 overs, their actual run rate is:
R = N ÷ 18
If this run rate increased by 50%, the new rate becomes:
New rate = 1.5 × R = 1.5 × (N ÷ 18)
At this new rate, in 12 overs, the runs scored would be:
Runs = New rate × 12 = 1.5 × (N ÷ 18) × 12
Simplifying:
Runs = (3N ÷ 2) × (2 ÷ 3) = N
So, both scenarios lead to a total of N runs being scored.
Conclusion:
The equation simplifies to an identity (N = N), which means no unique value for N can be determined. The given information is consistent but insufficient to calculate an exact number of runs and hence cannot be determined.
Hence Option (d) is the correct answer.
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