Question

The average age of P, Q, R, and S is 30 years. How old is R? 
Statement I - The sum of ages of P and R is 60 years. 
Statement II - S is 10 years younger than R.

• A. If the question can be answered with the help of statement I alone.
• B. If the question can be answered with the help of statement II alone.
• C. If both, statement I and statement II are needed to answer the question.
• D. If the question cannot be answered even with the help of both the statements.

Hint:

In problems involving averages and sums, combine equations to solve for unknowns.

Answer 1

The Correct Option is C

From Statement I: The sum of the ages of P and R is 60 years. This gives us the equation: \[ {P} + {R} = 60 \] But we still don’t know the individual ages of P and R or how they relate to Q and S. From Statement II: S is 10 years younger than R, which means: \[ {S} = {R} - 10 \] This helps us relate R and S, but without knowing the total sum of the ages or more specific information, we cannot determine R’s age from this statement alone. Combining both statements:
The average age of P, Q, R, and S is given as 30 years. This means the total sum of their ages is: \[ (P + Q + R + S) = 4 \times 30 = 120 \] We know that P + R = 60 and S = R - 10. Substituting these into the total sum equation: \[ 60 + Q + (R - 10) = 120 \] Simplifying: \[ Q + R + 50 = 120 \quad \Rightarrow \quad Q + R = 70 \] Now, combining this with the equation P + R = 60, we can find that R is 30 years old. Thus, both statements are needed to find the age of R.