Suppose you are designing an electronical musical instrument. The prototype syst

Question

Suppose you are designing an electronical musical instrument. The prototype system occasionally produces off-key notes, causing listeners towince and grimace. You have determined the cause of the problem is that the system becomes overwhelmed in processing the complicated input. You are thinking that if you could boost overall system performance by 12% (making it 12% faster than it is now), you could eliminate the problem. One option is to use a faster processor, if the processor accounts for 25% of the workload of this system, and you need to boost performance by 12%, how much faster does the new processor need to be?

Explanation / Answer

we need 12 % boost when processor accounts for 25 %.

let initial performance be x.

we want new performance be x + 12/100 x.

also the initial performance can be split into 0.25 x ( processor) and 0.75 x which is constant.

now 0.25 x changes , i.e. processor performance changes , let it be y.

=> 0.75 x + y = 1.12 x

=> y = 0.37 x

initially the processor was 0.25 x

so it becomes 0.37/0.25 times faster , i.e. 1.48 times or 48% faster.

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