Company $X$ has exactly two product lines and no other sources of revenue. If the consumer product line experiences a $k %$ increase in revenue (where $k$ is a positive integer) in 2015 from 2014 levels and the machine parts line experiences a $k %$ decrease in revenue in 2015 from 2014 levels, did Company X's overall revenue increase or decrease in 2015?
(1) In 2014, the consumer products line generated more revenue than the machine parts line.
(2) $k = 8$

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Solution

Given : Consumer product revenue is greater than machine parts revenue.
$C P R > M R P$
$C P R$ experiences $k$ % $= 8$ % increase
Profit $= \frac{8}{100} \times C P R$
$M P R$ experiences $8$ % decrease
Loss $= \frac{8}{100} \times M P R$
Total $= P r o f i t - L o s s = \frac{8}{100} (C P R - M P R)$
Since $C P R > M P R$
$C P R - M P R > 0$
Totally there is a positive profit.
So company revenue increases over all.

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Given : Consumer product revenue is greater than machine parts revenue.CPR>MRPCPR experiences k%=8% increaseProfit=8100×CPRMPR experiences 8% decreaseLoss=8100×MPRTotal=Profit−Loss=8100(CPR−MPR)Since CPR>MPRCPR−MPR>0Totally there is a positive profit.So company revenue increases over all.