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# If the ages of a husband, wife and their child are in the ratio 13 : 1

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If the ages of a husband, wife and their child are in the ratio 13 : 1  [#permalink]

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17 Jan 2020, 01:10
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84% (01:27) correct 16% (01:49) wrong based on 19 sessions

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If the ages of a husband, wife and their child are in the ratio 13 : 11 : 3 and the average age of the family of the three is 36 years, what is the difference between the ages of the husband and the wife?

A. 2
B. 4
C. 6
D. 8
E. 10

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Re: If the ages of a husband, wife and their child are in the ratio 13 : 1  [#permalink]

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17 Jan 2020, 05:07
If their average age is 36, the sum of their three ages is (3)(36) = 108. In the ratio 13:11:3, the parts add to 13+11+3 = 27, and since 108 = (4)(27), their actual ages are 4 times the numbers in the ratio, so are 52, 44 and 12. So the difference in the husband and wife's ages is 8.
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Re: If the ages of a husband, wife and their child are in the ratio 13 : 1  [#permalink]

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17 Jan 2020, 08:15
Bunuel wrote:
If the ages of a husband, wife and their child are in the ratio 13 : 11 : 3 and the average age of the family of the three is 36 years, what is the difference between the ages of the husband and the wife?

A. 2
B. 4
C. 6
D. 8
E. 10

Average age is $$\frac{13+11+3}{3} = 9$$

9 is represented as 36
1 is represented as 4
( 13-11) 2 is represented as 8, Answer must be (D)
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Re: If the ages of a husband, wife and their child are in the ratio 13 : 1  [#permalink]

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17 Jan 2020, 08:51
Bunuel wrote:
If the ages of a husband, wife and their child are in the ratio 13 : 11 : 3 and the average age of the family of the three is 36 years, what is the difference between the ages of the husband and the wife?

A. 2
B. 4
C. 6
D. 8
E. 10

Let the ages of husband, wife and child be 13x, 11x & 3x respectively
Average age = 27x/3 = 9x = 36
x= 4

Difference between ages of husband and wife = 13x - 11x = 2x = 8

IMO D

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Re: If the ages of a husband, wife and their child are in the ratio 13 : 1  [#permalink]

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17 Jan 2020, 10:17
The ages of the ages of a husband, wife and their child are 13x, 11x, 3x respectively.
Average of the ages = 13x +11x + 3x/3 = 27x/3 = 9x
As per question, 9x = 36
X = 4
difference between the ages of the husband and the wife = 13x -11x = 2x =2*4 = 8 years(D)
Re: If the ages of a husband, wife and their child are in the ratio 13 : 1   [#permalink] 17 Jan 2020, 10:17
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