Discussion
From 2018 to 2019, Mohan’s annual salary increased by 10 percent and Arun’s annual salary decreased by 5 percent. If their annual salaries were equal in 2019, then Arun’s annual salary in 2018 was what percent greater than Mohan’s annual salary in 2018 ?
Answer: C
Arun's 2018 salary was about 15.78 percent greater than Mohan's.
Let Mohan's 2018 salary be M and Arun's A. In 2019 they were equal:
\[ \begin{aligned} 1.10\,M &= 0.95\,A \\ \frac{A}{M} &= \frac{1.10}{0.95} = \frac{22}{19} \\ &\approx 1.1579 \end{aligned} \]
So Arun earned about 15.79% more, which the paper prints, cut at two decimals, as 15·78.
Simply adding the two changes gives 15%, close but not offered. 10·98 is close to Mohan's 10% rise alone and ignores Arun's 5% fall; 16·91 and 13·34 do not fit the equation above.
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