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 wrote: ↑

Tue Jun 02, 2020 7:46 am

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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Vincen wrote: ↑

Tue Jun 02, 2020 7:46 am

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