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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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20 May 2017, 06:21
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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

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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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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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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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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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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

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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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