Given below is a question followed by two statements, I and II, each containing some information. Decide which of the statements are sufficient to answer the question.
The difference between father's age and son's age is 21 years now. What is the present age of the son?
Statements:
I. After five years, the ratio of father's age to that of the son would be 5:2.
II. The sum of father's age and son's age after five years would be 66 years.
- AStatement I alone is sufficient.
- BStatement II alone is sufficient.
- CEither statement I alone or statement II alone is sufficient.
- DBoth statements I and II together are needed.
Solution & Step-by-step Explanation
Let the present age of the father be and the son be .
Given:
From Statement I:
After years, the ratio becomes .
Substitute :
Thus, Statement I alone is sufficient.
From Statement II:
The sum after years is .
We have a system of linear equations:
Adding them gives , which can be solved to find .
Thus, Statement II alone is also sufficient.
Since either statement independently provides the answer, the correct choice is C.
Given:
From Statement I:
After years, the ratio becomes .
Substitute :
Thus, Statement I alone is sufficient.
From Statement II:
The sum after years is .
We have a system of linear equations:
Adding them gives , which can be solved to find .
Thus, Statement II alone is also sufficient.
Since either statement independently provides the answer, the correct choice is C.