Question

The ratio of the ages of A and B is 5:7. After 8 years, the ratio becomes 7:9. What is B's present age?

• A. 28 years
• B. 35 years
• C. 42 years
• D. 49 years

Hint:

Look at the ratio differences: the initial ratio is 5:7 (difference is 2 units) and the final ratio is 7:9 (difference is 2 units).
Since the difference is constant, the increase in each person's ratio is from 5 to 7 (2 units) and 7 to 9 (2 units).
This increase of 2 units corresponds exactly to the 8 years that passed.
Therefore, 2 units = 8 years, which means 1 unit = 4 years.
We can compute B's age directly as $7 \text{ units} \times 4 = 28 \text{ years}$ without setting up equations.

Answer 1

The Correct Option is A

Step 1: Set up the present ages.
Let the common multiple be $x$. Then A is $5x$ and B is $7x$ right now, because their ratio is $5:7$.

Step 2: Add 8 years to each age.
After $8$ years, A becomes $5x + 8$ and B becomes $7x + 8$.

Step 3: Use the new ratio.
We are told the new ratio is $7:9$, so \[ \frac{5x+8}{7x+8} = \frac{7}{9} \]

Step 4: Cross multiply.
$9(5x+8) = 7(7x+8)$, which gives $45x + 72 = 49x + 56$.

Step 5: Solve for x.
Bring like terms together, $72 - 56 = 49x - 45x$, so $16 = 4x$ and $x = 4$.

Step 6: Find B's present age.
B is $7x$, so $7 \times 4 = 28$.

Step 7: State the answer.
B is $28$ years old today. \[ \boxed{28 \text{ years}} \]