Final answer:
The overall speedup of a system after a processor upgrade with a 100% increase in throughput for tasks that take up 40% of its time is calculated to be a 25% improvement in speed, which does not match any of the provided answers. There may be an error in the question or its options.
Step-by-step explanation:
Calculating the overall speedup of a system after a processor upgrade is a problem that falls under the category of performance improvement in computing. If a system spends 40% of its time in calculations and receives a processor upgrade that doubles the throughput (a 100% increase) for those calculations, we can use Amdahl's law to find the overall speedup.
The formula for calculating the speedup is given as:
Speedup = 1 / [(1 - Fraction_enhanced) + (Fraction_enhanced / Speedup_enhanced)]
Here Fraction_enhanced is the fraction of time the system is improved by speedup due to the processor upgrade (0.40 or 40%), and Speedup_enhanced is the factor by which the processor improves (which is 2 in this case, as a 100% increase means a doubling of performance).
Applying these values:
Speedup = 1 / [(1 - 0.40) + (0.40 / 2)]
Speedup = 1 / [0.60 + 0.20]
Speedup = 1 / 0.80
Speedup = 1.25
As a percentage, this speedup is a 25% overall improvement. However, since the question asks for the answer in integer percent and the provided options do not include 25%, there might be a mistake in the provided options or the question itself.