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(A) Let the total number of candidates who applied be $5x$.Since the ratio of selected to unselected candidates is $4:1$,the number of selected candid

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$1650$

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(A) Let the total number of candidates who applied be $5x$.Since the ratio of selected to unselected candidates is $4:1$,the number of selected candidates is $4x$ and the number of unselected candidates is $x$.According to the problem,if $90$ fewer candidates had applied,the new total would be $5x - 90$.If $20$ fewer candidates were selected,the new number of selected candidates would be $4x - 20$.The new number of unselected candidates would be $(5x - 90) - (4x - 20) = x - 70$.Given the new ratio is $5:1$,we have the equation:$\frac{4x - 20}{x - 70} = \frac{5}{1}$$4x - 20 = 5(x - 70)$$4x - 20 = 5x - 350$$x = 350 - 20 = 330$Therefore,the total number of candidates who applied is $5x = 5 	imes 330 = 1650$.

In an army selection process,the ratio of selected to unselected candidates was $4:1$. If $90$ less had applied and $20$ less were selected,the ratio of selected to unselected candidates would have been $5:1$. How many candidates had applied for the process?

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