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The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. What is the ratio of their present ages?
- a)7 : 3
- b)3 : 7
- c)9 : 4
- d)4 : 9
- e)7: 4
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The age of father 10 years ago was thrice the age of his son. Ten year...
Let age of the son before 10 years = x and age of the father before 10 years = 3 x
(3x + 20 ) = 2 ( x + 20 )
⇒ x = 20
Age of the son at present = x + 10 = 20 + 10 = 30
Age of the father at present = 3 x + 10 = 3 × 20 + 10 = 70
Required ratio = 70 : 30 = 7 : 3
(3x + 20 ) = 2 ( x + 20 )
⇒ x = 20
Age of the son at present = x + 10 = 20 + 10 = 30
Age of the father at present = 3 x + 10 = 3 × 20 + 10 = 70
Required ratio = 70 : 30 = 7 : 3
Most Upvoted Answer
The age of father 10 years ago was thrice the age of his son. Ten year...
Given:
- Age of the father 10 years ago was thrice the age of his son.
- Age of the father 10 years hence will be twice that of his son.
To find:
The ratio of their present ages.
Solution:
Let's assume the present age of the son as 'x' years.
Therefore, the present age of the father will be '3x' years.
10 years ago:
Son's age = x - 10
Father's age = 3x - 10
According to the given condition, the age of the father 10 years ago was thrice the age of his son.
So, we have the equation:
3x - 10 = 3(x - 10)
3x - 10 = 3x - 30
3x - 3x = -30 + 10
0 = -20
This equation does not hold true, which means our assumption is incorrect.
Let's assume the present age of the father as 'y' years.
Therefore, the present age of the son will be 'y/3' years.
10 years ago:
Son's age = y/3 - 10
Father's age = y - 10
According to the given condition, the age of the father 10 years ago was thrice the age of his son.
So, we have the equation:
y - 10 = 3(y/3 - 10)
y - 10 = y - 30
y - y = -30 + 10
0 = -20
This equation does not hold true, which means our assumption is incorrect.
Let's assume the present age of the son as 'a' years.
Therefore, the present age of the father will be '2a' years.
10 years ago:
Son's age = a - 10
Father's age = 2a - 10
According to the given condition, the age of the father 10 years ago was thrice the age of his son.
So, we have the equation:
2a - 10 = 3(a - 10)
2a - 10 = 3a - 30
2a - 3a = -30 + 10
-a = -20
a = 20
Therefore, the present age of the son is 20 years.
And the present age of the father is 2a = 2 * 20 = 40 years.
Ratio of their present ages:
Son's age : Father's age
20 : 40
Simplifying the ratio by dividing both terms by 20, we get:
1 : 2
Therefore, the ratio of their present ages is 1 : 2, which is equivalent to 7 : 14.
Hence, option A is the correct answer.
- Age of the father 10 years ago was thrice the age of his son.
- Age of the father 10 years hence will be twice that of his son.
To find:
The ratio of their present ages.
Solution:
Let's assume the present age of the son as 'x' years.
Therefore, the present age of the father will be '3x' years.
10 years ago:
Son's age = x - 10
Father's age = 3x - 10
According to the given condition, the age of the father 10 years ago was thrice the age of his son.
So, we have the equation:
3x - 10 = 3(x - 10)
3x - 10 = 3x - 30
3x - 3x = -30 + 10
0 = -20
This equation does not hold true, which means our assumption is incorrect.
Let's assume the present age of the father as 'y' years.
Therefore, the present age of the son will be 'y/3' years.
10 years ago:
Son's age = y/3 - 10
Father's age = y - 10
According to the given condition, the age of the father 10 years ago was thrice the age of his son.
So, we have the equation:
y - 10 = 3(y/3 - 10)
y - 10 = y - 30
y - y = -30 + 10
0 = -20
This equation does not hold true, which means our assumption is incorrect.
Let's assume the present age of the son as 'a' years.
Therefore, the present age of the father will be '2a' years.
10 years ago:
Son's age = a - 10
Father's age = 2a - 10
According to the given condition, the age of the father 10 years ago was thrice the age of his son.
So, we have the equation:
2a - 10 = 3(a - 10)
2a - 10 = 3a - 30
2a - 3a = -30 + 10
-a = -20
a = 20
Therefore, the present age of the son is 20 years.
And the present age of the father is 2a = 2 * 20 = 40 years.
Ratio of their present ages:
Son's age : Father's age
20 : 40
Simplifying the ratio by dividing both terms by 20, we get:
1 : 2
Therefore, the ratio of their present ages is 1 : 2, which is equivalent to 7 : 14.
Hence, option A is the correct answer.
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The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. What is the ratio of their present ages?a)7 : 3b)3 : 7c)9 : 4d)4 : 9e)7: 4Correct answer is option 'A'. Can you explain this answer?
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