A is 25 years younger than B. The age of B would be double the age of C after 15 years. The current age of B is three times the current age of C. What is the current age of A?

The correct answer is 20 years.

Let's define variables for the current ages:

Let the current age of B = B
Let the current age of C = C
Let the current age of A = A

Step 1 – Translate each condition into an equation.

Condition 1: "A is 25 years younger than B."

A=B-25 \text{... (i)}

Condition 2: "The current age of B is three times the current age of C."

B=3C \text{... (ii)}

Condition 3: "The age of B would be double the age of C after 15 years." This means: after 15 years, B's age = 2 × (C's age after 15 years).

(B+15)=2(C+15) \text{... (iii)}

Step 2 – Use equations (ii) and (iii) to find B and C.

From equation (ii), we know C=\frac{B}{3}. Substitute this into equation (iii):

B+15=2(\frac{B}{3}+15)

Expand the right-hand side:

B+15=\frac{2B}{3}+30

Bring the B terms to one side and constants to the other:

B-\frac{2B}{3}=30-15

\frac{3B-2B}{3}=15

\frac{B}{3}=15

B=45\text{ years}

Now find C using equation (ii):

C=\frac{45}{3}=15\text{ years}

Step 3 – Verify Condition 3 (sanity check).

After 15 years: B = 45 + 15 = 60, and C = 15 + 15 = 30. Is 60 = 2 × 30? ✓ Yes!

Step 4 – Find the current age of A using equation (i).

A=B-25=45-25=20\text{ years}

Therefore, the current age of A is 20 years.