The ratio of the son’s age to the father’s age is 1 ∶ 4. The product of their ages is 196. The ratio of their ages after 5 years will be?
A. 4 ∶ 13
B. 3 ∶ 10
C. 4 ∶ 11
D. 5 ∶ 14
Explanation:
Math MCQ: Ratio of Ages After 5 Years
Let’s solve the problem step by step.
Given:
The ratio of son’s age to father’s age = 1 ∶ 4
The product of their ages = 196
Let “x” represent the age of the son, and “4x” represent the age of the father since the ratio of their ages is 1 ∶ 4.
According to the given information, their ages’ product is 196:
⇒ x × 4x = 196
⇒ 4x2 = 196
⇒ x2 = 49 Taking the square root of both sides:
⇒ x = √49
⇒ x = 7
So, the present age of the son is 7 years, and the present age of the father is 4x = 4 * 7 = 28 years.
Now, let’s find their ages after 5 years:
⇒ Son’s age after 5 years = 7 + 5 = 12 years
⇒ Father’s age after 5 years = 28 + 5 = 33 years
The ratio of their ages after 5 years is:
⇒ Age of Son : Age of Father = 12 ∶ 33
To simplify the ratio, we can divide both sides by their common factor, which is 3:
⇒ Age of Son : Age of Father = 4 ∶ 11
Therefore, the ratio of the son’s age to the father’s age after 5 years will be 4 ∶ 11.
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