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23 Jun 2020, 10:27
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
46% (03:28) correct
54%
(02:51)
wrong
based on 52
sessions
History
Date
Time
Result
Not Attempted Yet
The average age of a couple was 24 years. After their 1st and 2nd children (twins) were born, the average age of the family became 13.5 years. The average age of the family just after 3rd child was born was 13.2 years. The average age of the family after 4th child was born was 16 years. The current average age of the family is 19 years. What is the current age of the twin children?
A. 11 years
B. 12 years
C. 13 years
D. 14 years
E. 15 years
A. 11 years
B. 12 years
C. 13 years
D. 14 years
E. 15 years
23 Jun 2020, 13:41
Kudos
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Sum of the age of couple when twins were born = 13.5*4 = 54
Age of twins when 3rd child was born = \(\frac{(13.2*5) - 54}{4} = \frac{66-54}{4} = 3\) years
Age of twins when 4th child was born = \(3+ \frac{(16*6) - 66}{5} =3+ \frac{96-66}{5} = 9\)
Age of twins now= \(9+\frac{(19*6) - 96}{6} =9+ \frac{18}{6} = 12\)
Age of twins when 3rd child was born = \(\frac{(13.2*5) - 54}{4} = \frac{66-54}{4} = 3\) years
Age of twins when 4th child was born = \(3+ \frac{(16*6) - 66}{5} =3+ \frac{96-66}{5} = 9\)
Age of twins now= \(9+\frac{(19*6) - 96}{6} =9+ \frac{18}{6} = 12\)
Bunuel
27 Jun 2020, 05:58
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Bunuel
Solution:
We can let each parent be 24 years old before giving birth to any children. So the sum of their ages was 48.
After the twins were born, the sum of the ages of all 4 members of the family is 13.5 x 4 = 54. Since the twins were 0 year old, the parents must be 27 years old each.
After the third child was born, the sum of the ages of all 5 members of the family is 13.2 x 5 = 66. Since the third child was 0 year old and if the twins were x years old then, we can create the equation:
(27 + x) + (27 + x) + x + x = 66
54 + 4x = 66
4x = 12
x = 3
So the twins were 3 years old and the parents were 30 years old each when the third child was born.
After the fourth child was born, the sum of the ages of all 6 members of the family is 16 x 6 = 96. Since the fourth child was 0 year old and if the third child was y years old then, we can create the equation:
(30 + y) + (30 + y) + (3 + y) + (3 + y) + y = 96
66 + 5y = 96
5y = 30
y = 6
So the third child was 6 years old, the twins were 9 years old and the parents were 36 years old each when the fourth child was born.
Finally, we are asked for the age of the twins when the current average age of the family is 19 years. But notice that 19 is 3 more than 16, that is, each family member must grow 3 years older in order to lift the average age from 16 to 19. Therefore, the twins are 9 + 3 = 12 years old now.
Answer: B
