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The income of Q is 25% less than the income of R. The income of P is 20% higher than that of Q. What percent less is P’s income from R’s income?
Let the incomes of P, Q, and R be $$p,q$$ and $$r,$$ respectively.
We are given that the value of $$q$$ is $$25\%$$ less than $$r$$. So, the value of $$q$$ can be written as,
$$q\ =\left(1\ -\ \dfrac{25}{100}\right)r=\dfrac{3}{4}r$$.
We are also given that $$p$$ is $$20\%$$ higher than $$q$$. So, the value of $$p$$ can be written as,
$$p=\left(1\ +\ \dfrac{20}{100}\right)q=\dfrac{6}{5}q=\dfrac{6}{5}\times\ \dfrac{3}{4}r=\dfrac{9}{10}r$$
The percentage by which the salary of $$p$$ is less than $$r$$ can be calculated as,
Percentage $$=$$ $$\dfrac{r\ -\ p}{r}\times\ 100\ =\ \dfrac{\left(r\ -\ \dfrac{9}{10}r\right)}{r}\times\ 100\ =\ \dfrac{1}{10}\times\ 100\ =\ 10\%$$
Hence, the correct answer is option B.
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