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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


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

Originally posted by gracie on 25 Dec 2017, 12:30.
Last edited by gracie on 25 Dec 2017, 13:49, 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]
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]
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]
1
Kudos
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]
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]
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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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