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The ratio of two numbers is 10 and their difference is 18. What is the

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The ratio of two numbers is 10 and their difference is 18. What is the  [#permalink]

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New post 20 May 2017, 06:21
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Re: The ratio of two numbers is 10 and their difference is 18. What is the  [#permalink]

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New post 20 May 2017, 07:00
The ratio is 10 or 10:1. Let the two numbers be 10x and x.

Given 10x - x = 18. Solve to get x=2

Hence A
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Re: The ratio of two numbers is 10 and their difference is 18. What is the  [#permalink]

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New post 20 May 2017, 08:16
Bunuel wrote:
The ratio of two numbers is 10 and their difference is 18. What is the value of the smaller number?

(A) 2
(B) 5
(C) 10
(D) 21
(E) 27

Quote:
The ratio of two numbers is 10


\(\frac{a}{b} = 10\) ---------------> (1)

Quote:
and their difference is 18


\(a - b = 18\) ---------------> (2)

Or, \(a = 18 + b\) ---------------->(3)

Putting (3) in (1)

\(\frac{18+b}{b} = 10\)

Or, \(18 + b = 10b\)

Or, \(9b = 18\)

So, \(b = 2\) ----------------> (4)

Putting (4) in ( 2 )

\(a - 2 = 18\)

So, \(a = 16\)

Thus, the value of the smaller number is (A) 2
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Re: The ratio of two numbers is 10 and their difference is 18. What is the  [#permalink]

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New post 20 May 2017, 11:46
If the ratio of the two numbers is 10,
The larger number by the smaller number will be 10:1
The possible combinations along with the answer choices for smaller number are
(20,2),(50,5).... The only possibility which gives a difference of 18 is Option A
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Re: The ratio of two numbers is 10 and their difference is 18. What is the  [#permalink]

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New post 20 May 2017, 12:21
The ratio of two numbers is 10 and their difference is 18. What is the value of the smaller number?
(A) 2
(B) 5
(C) 10
(D) 21
(E) 27

Let one number be X and other number be Y.
Ratio of X to Y = \(\frac{X}{Y}\) = 10 ------------- (i)
Difference of X and Y = X - Y = 18 ------------- (ii)
From equation (i) ; X = 10Y
Substituting X in equation (ii);
10Y - Y = 9Y = 18; Y = 2.
Hence X = 20
Therefore Smaller number is 2
Answer A...

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Re: The ratio of two numbers is 10 and their difference is 18. What is the &nbs [#permalink] 20 May 2017, 12:21
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