The ratio of \(a\) to \(b\) is 4 to 5, where \(a\) and \(b\) are positive. If \(x\) equals \(a\) increased by 25 percent

[Vincen]

The ratio of \(a\) to \(b\) is 4 to 5, where \(a\) and \(b\) are positive. If \(x\) equals \(a\) increased by 25 percent of \(a,\) and \(m\) equals \(b\) decreased by 20 percent of \(b,\) what is the value of \(\dfrac{m}{x}?\)

A. 2/5
B. 3/4
C. 4/5
D. 5/4
E. 3/2

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

[Jay@ManhattanReview]

The ratio of \(a\) to \(b\) is 4 to 5, where \(a\) and \(b\) are positive. If \(x\) equals \(a\) increased by 25 percent of \(a,\) and \(m\) equals \(b\) decreased by 20 percent of \(b,\) what is the value of \(\dfrac{m}{x}?\)

A. 2/5
B. 3/4
C. 4/5
D. 5/4
E. 3/2

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

Given that \(a\) to \(b\) is 4 to 5, where \(a\) and \(b\) are positive, say \(a=4\) and \(b=5\).

So, \(x=4+25\%\ of\ 4=5\ \) and \(m=5-20\%\ of\ 5=4\). Thus, the value of \(\dfrac{m}{x}=\dfrac{4}{5}\).

The correct answer: C

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

The ratio of \(a\) to \(b\) is 4 to 5, where \(a\) and \(b\) are positive. If \(x\) equals \(a\) increased by 25 percent of \(a,\) and \(m\) equals \(b\) decreased by 20 percent of \(b,\) what is the value of \(\dfrac{m}{x}?\)

A. 2/5
B. 3/4
C. 4/5
D. 5/4
E. 3/2

[spoiler]OA=C[/spoiler]

Solution:

We are given that a : b = 4n : 5n.

We are also given that x equals a increased by 25 percent of a, and thus:

x = a + 0.25a

x = 1.25a

x = 1.25(4n)

x = 5n

We are also given that m equals b decreased by 20 percent of b, and thus:

m = b - 0.2b

m = 0.8b

m = 0.8(5n)

m = 4n

Thus, m/x = 4n/5n = 4/5.

Answer: C