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# The ratio of a to b is 4 to 5, where a and b are positive. If x equals

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Math Expert
Joined: 02 Sep 2009
Posts: 55618
The ratio of a to b is 4 to 5, where a and b are positive. If x equals  [#permalink]

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03 Feb 2015, 09:49
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35% (medium)

Question Stats:

74% (01:38) correct 26% (01:51) wrong based on 231 sessions

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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 m/x?

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

Kudos for a correct solution.

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Posts: 46
Re: The ratio of a to b is 4 to 5, where a and b are positive. If x equals  [#permalink]

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03 Feb 2015, 10:03
1
x equals a increased by 25 percent of a => x = a + 25%a = 1.25a
m equals b decreased by 20 percent of b => m = b - 20%b = 0.8b
m/x = 0.8b/1.25a
Putting the value of b/a = 5/4 we get m/x = 4/5
[C]
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Re: The ratio of a to b is 4 to 5, where a and b are positive. If x equals  [#permalink]

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03 Feb 2015, 10:30
1
x = 1,25 a
m = b+*0,8

A:B
4:5

0.8 * 5/9 = 8/10 * 5/9 = 4/9
1,25 * 4/9 = 125/100 * 4/9 = 5/9

>> m/x = 4:5 --> Answer C
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Re: The ratio of a to b is 4 to 5, where a and b are positive. If x equals  [#permalink]

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03 Feb 2015, 19:31
1
Bunuel wrote:
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 m/x?

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

Kudos for a correct solution.

From the question stem we can see that a:b is 4:5... which is the same as a/b = 4/5. x = a + 0.25a = 1.25a, this is the same as 5/4*(a). m = b - 0.2b = 0.8b, this is the same as 4/5*(b).

m/x = (4/5*(b))/(5/4*(a))..... is equal to (4b/5)/(5a/4).......this gives us (4b/5)*(4/5a) = (16b)/(25)a. (16b)/(25a) = (16/25)*(b/a) = (16/25)*(5/4) = 4/5.

I think the answer is C.

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Re: The ratio of a to b is 4 to 5, where a and b are positive. If x equals  [#permalink]

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09 Feb 2015, 04:52
Bunuel wrote:
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 m/x?

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

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

The correct response is (C). In multi-step problems with numerous variables, it’s a good idea to pick numbers. Since the ratio of a to b is 4 to 5 and a and b are positive, let’s say a = 4 and b = 5. Now we can translate the rest of the problem from English into algebra: “x equals a increased by 25 percent of a” x = 4 + .25(4) x = 4 + 1 x = 5 “m equals b decreased by 20 percent of b” m = 5 – .20(5) m = 5 – 1 m = 4 Therefore, m/x = 4/5.
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Re: The ratio of a to b is 4 to 5, where a and b are positive. If x equals  [#permalink]

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14 Jun 2017, 22:59
1
Bunuel wrote:
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 m/x?

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

Kudos for a correct solution.

X = 4* 125/100 = 5
M = 5* 80/100 = 4

Ratio = 4/5
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Re: The ratio of a to b is 4 to 5, where a and b are positive. If x equals  [#permalink]

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15 Jun 2017, 08:27
Bunuel wrote:
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 m/x?

A. 2/5
B. 3/4
C. 4/5
D. 5/4
E. 3/2
Kudos for a correct solution.

a = 4 & b = 5

Quote:
If x equals a increased by 25 percent of a

x = 5

Quote:
m equals b decreased by 20 percent of b

m = 4

Quote:
what is the value of m/x?

$$\frac{4}{5}$$

Thus, answer will be (C) $$\frac{4}{5}$$
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Re: The ratio of a to b is 4 to 5, where a and b are positive. If x equals  [#permalink]

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06 Jul 2017, 17:27
Bunuel wrote:
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 m/x?

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

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.

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Re: The ratio of a to b is 4 to 5, where a and b are positive. If x equals  [#permalink]

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16 Sep 2018, 21:52
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Re: The ratio of a to b is 4 to 5, where a and b are positive. If x equals   [#permalink] 16 Sep 2018, 21:52
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