Question

What was the ratio between the ages of P and Q four years ago? I. The ratio between the present ages of P and Q is 3 : 4. II. The ratio between the present ages of Q and R is 4 : 5.

• A. if the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
• B. if the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
• C. if the data in both the statements I and II together are not sufficient to answer the question.
• D. if the data in both the statements I and II together are necessary to answer the question.

Hint:

When dealing with ratios, check if you have enough relationships to link all variables involved. If not, the information might be insufficient.

Answer 1

The Correct Option is C

Step 1: From statement I, the ratio of the present ages of P and Q is 3:4. Let the present ages of P and Q be \( 3x \) and \( 4x \), respectively. 
Step 2: From statement II, the ratio of the present ages of Q and R is 4:5. Let the present ages of Q and R be \( 4y \) and \( 5y \), respectively. 
Step 3: We have two variables \( x \) and \( y \), and no further relationship is provided between \( x \) and \( y \). Therefore, we cannot determine the ratio of P’s and Q’s ages four years ago with the information given in both statements. Thus, the answer is \( \boxed{{C}} \).