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The ratio of two numbers is 7/6. If the smaller of the two numbers is

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The ratio of two numbers is 7/6. If the smaller of the two numbers is [#permalink]

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New post 25 Dec 2017, 00:09
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The ratio of two numbers is 7/6. If the smaller of the two numbers is decreased by two the ratio is 7/5, what is the larger number?

A. 28
B. 21
C. 14
D. 12
E. 10
[Reveal] Spoiler: OA

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Re: The ratio of two numbers is 7/6. If the smaller of the two numbers is [#permalink]

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New post 25 Dec 2017, 00:49
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Bunuel wrote:
The ratio of two numbers is 7/6. If the smaller of the two numbers is decreased by two the ratio is 7/5, what is the larger number?

A. 28
B. 21
C. 14
D. 12
E. 10


Questions which change an old to a new ratio can often be tricky so we'll use the answers.
This is an Alternative approach.

We'll start with the median answer - 14.
If the larger number is 14 the smaller is 14* (6/7) = 12.
If this is decreased by 2 to 10 then the new ratio is 14/10 = 7/5.
Yes!
(C) is our answer.

* Had (C) not been correct we would have gone up to (B) or down to (D) depending on if we needed to increase or decrease our answer.
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The ratio of two numbers is 7/6. If the smaller of the two numbers is [#permalink]

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Bunuel wrote:
The ratio of two numbers is 7/6. If the smaller of the two numbers is decreased by two the ratio is 7/5, what is the larger number?

A. 28
B. 21
C. 14
D. 12
E. 10

1) Set up the original ratio with a multiplier, x
The ratio of two numbers is 7/6 : \(\frac{7x}{6x}\)

2) Set up the equation*
The smaller number is decreased by two (LHS):
\(\frac{7x}{6x-2}\)
The new ratio is \(\frac{7}{5}\) (RHS), so
\(\frac{7x}{6x-2} = \frac{7}{5}\)

\(5(7x) = 7(6x - 2)\)
\(35x = 42x - 14\)
\(14 = 7x\)
\(x = 2\)

That multiplier, x, is only for original ratio, \(\frac{7x}{6x}\)

3) Larger number's value? x = 2
Larger number = 7x = (7)(2) = 14

Answer C

*the number added to 6x and the numbers in the new ratio are just numbers, i.e., not accompanied by any multiplier x
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The ratio of two numbers is 7/6. If the smaller of the two numbers is [#permalink]

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New post 25 Dec 2017, 11:30
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Bunuel wrote:
The ratio of two numbers is 7/6. If the smaller of the two numbers is decreased by two the ratio is 7/5, what is the larger number?

A. 28
B. 21
C. 14
D. 12
E. 10


(7/5)/(7/6)=6/5
6/5=[x/(y-2)]/(x/y)➡
5xy=6xy-12x➡
y=12
x=14
C

Last edited by gracie on 25 Dec 2017, 12:49, edited 5 times in total.
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Re: The ratio of two numbers is 7/6. If the smaller of the two numbers is [#permalink]

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New post 25 Dec 2017, 11:42
Let, small number = S, Big number= B. Given, B/S= 7/6 (big over small ratio has to be greater than 1)
Implies 6B=7S or 6B-7S=0.....(i)

Now, small number decreased by 2. B/(S-2)= 7/5 implies 5B-7S=-14....(ii)

Now you have 2 linear equations with 2 unknowns, B and S. Solve to get B=14, hence C.
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Re: The ratio of two numbers is 7/6. If the smaller of the two numbers is [#permalink]

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New post 25 Dec 2017, 16:59
Bunuel wrote:
The ratio of two numbers is 7/6. If the smaller of the two numbers is decreased by two the ratio is 7/5, what is the larger number?

A. 28
B. 21
C. 14
D. 12
E. 10


Lets call the larger \(a\) and the smaller \(b\).

First equation: \(\frac{a}{b}=\frac{7}{6}\), then \(a=\frac{7b}{6}\).

Second equation: \(\frac{a}{b-2}=\frac{7}{5}\), then \(5a=7b-14\).

Solve for \(b\) by substituting \(a\) in the second equation: \(5a=7b-14\), becomes \(5*\frac{7b}{6}=7b-14\), \(35b=42b-84\), \(-7b=-84\), \(b=12\)

Solve for \(a\) by substituting \(b\) in the first equation: \(a=\frac{7b}{6}=\frac{7(12)}{6}=7*2=14\)

(C) is the answer.
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The ratio of two numbers is 7/6. If the smaller of the two numbers is [#permalink]

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New post 26 Dec 2017, 01:44
Bunuel wrote:
The ratio of two numbers is 7/6. If the smaller of the two numbers is decreased by two the ratio is 7/5, what is the larger number?

A. 28
B. 21
C. 14
D. 12
E. 10


Another approach

Let small number = S, large number= L

Old ratio: L/S= 7/6= 14/12 = 21/18 = 28/24

New ratio: L/S = 7/5 =14 /10 = 21/15 = 28/20

Compare the old and new such that the small number decreased by 2

The large number = 14

Answer: C
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Re: The ratio of two numbers is 7/6. If the smaller of the two numbers is [#permalink]

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New post 26 Dec 2017, 21:56
The answer is C
As 14/12 = 7/6 ads after decreasing the smallest by 2 becomes 14/10= 7/5 so the largest number is
C which is 14


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Re: The ratio of two numbers is 7/6. If the smaller of the two numbers is   [#permalink] 26 Dec 2017, 21:56
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