Question

A is 3 years younger than B. B is 7 years older than C. The average of C and D's age is 25. If D's age is 40 then what is the age of A?

• A. 17 years
• B. 14 years
• C. 10 years
• D. 40 years

Hint:

Work backwards from the known absolute value ($D = 40$) to find $C$, then use $C$ to find $B$, and finally $B$ to find $A$. This sequential substitution avoids any algebraic errors.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This problem requires setting up a series of linear equations linking the ages of four individuals.
Detailed Explanation:
Let the ages of A, B, C, and D be represented by their respective letters.
From the problem statements:
1. $A = B - 3$
2. $B = C + 7$
3. The average of C and D is 25: \[ \frac{C + D}{2} = 25 \implies C + D = 50 \] We are given that D's age is 40: \[ C + 40 = 50 \implies C = 10 \text{ years} \] Substitute $C = 10$ into the equation for B's age: \[ B = 10 + 7 = 17 \text{ years} \] Substitute $B = 17$ into the equation for A's age: \[ A = 17 - 3 = 14 \text{ years} \] Therefore, the age of A is 14 years.

Step 2: Final Answer:
The age of A is 14 years, matching Option (B).