Re: In year 1990, the wages of employees in a company Z was $x. The wage
[#permalink]
06 Dec 2024, 14:35
In year 1990 the wages of employees in company $\(X\)$ were $\(\$ x\)$. The wages increased by $\(15 \%\)$ during the time period 1990-1995 \& the increase was $\(30 \%\)$ for the period 1990-2000; we need to compare the percentage increase in wages from 1995-2000 with $\(15 \%\)$.
Let the percentage increase in wages from 1995-2000 be $\(\mathrm{x} \%\)$.
When there are two successive changes on a single value say $\(a \%\)$ and then $\(b \%\)$, the net percentage change on the value is of $\(\left(a+b+\frac{a b}{100}\right) \%\)$.
Here the two successive changes on wages from 1990-1995 \& 1995-2000 are of $\(15 \%\)$ and $\(\mathrm{x} \%\)$ respectively and the net change from $1990-2000$ is given to be $\(30 \%\)$, so we get $\(\left(15+x+\frac{15 \times x}{100}\right) \%=30 \%\)$ which clearly imply that the value of $\(x\)$ must be less than $\(15 \%\)$ (If $\(x=15 \%\)$ the net change would be greater than $\(30 \%\)$ ).
Hence column B quantity is greater than column A quantity, so the answer is (B).