Question

Four years ago, ages of A and B were respectively thrice and twice that of the age of C. If the total of their ages is 48, then the present age of B is.

• A. 16 years
• B. 22 years
• C. 10 years
• D. 12 years

Hint:

In age-related problems, express the ages of all individuals in terms of one variable and solve using simple algebraic equations.

Answer 1

The Correct Option is A

Let the present ages of A, B, and C be \( x \), \( y \), and \( z \) respectively. Step 1: Express the ages of A, B, and C four years ago.
- Four years ago, age of A = \( x - 4 \)
- Four years ago, age of B = \( y - 4 \)
- Four years ago, age of C = \( z - 4 \) According to the problem:
- Age of A was thrice that of C four years ago, i.e., \( x - 4 = 3(z - 4) \)
- Age of B was twice that of C four years ago, i.e., \( y - 4 = 2(z - 4) \)

Step 2: Set up the equation for total age.
The total of their ages is 48: \[ % Option (x) + (y) + (z) = 48 \]

Step 3: Solve the system of equations.
From the first equation, we get: \[ x - 4 = 3(z - 4) \quad \Rightarrow \quad x = 3z - 8 \] From the second equation: \[ y - 4 = 2(z - 4) \quad \Rightarrow \quad y = 2z - 4 \] Substitute the values of \( x \) and \( y \) into the total age equation: \[ (3z - 8) + (2z - 4) + z = 48 \] Simplify the equation: \[ 3z + 2z + z - 8 - 4 = 48 \] \[ 6z - 12 = 48 \quad \Rightarrow \quad 6z = 60 \quad \Rightarrow \quad z = 10 \]

Step 4: Calculate the present age of B.
From the equation \( y = 2z - 4 \): \[ y = 2(10) - 4 = 20 - 4 = 16 \]

Step 5: Final Answer
The present age of B is 16 years. Final Answer: The correct answer is (a) 16 years.