Question

If the ratio of the ages of A and B is 3:5 and their sum is 40 years, what is the age of B?

• A. 15 years
• B. 20 years
• C. 25 years
• D. 30 years

Hint:

For ratio problems, express quantities as multiples of a variable (e.g., \( 3x, 5x \)), set up an equation based on the given sum, and solve for the variable.

Answer 1

The Correct Option is C

The objective is to determine B's age, given the ratio of A's and B's ages and their combined age.

1. Core Concepts:

- Ratio of Ages: A and B's ages are in the proportion 3:5.
- Total Age: The sum of their ages is 40 years.
- The ratio allows us to represent their ages using a shared variable.

2. Provided Data:

- Age ratio = 3:5
- Sum of ages = 40 years

3. Age Calculation:

Let \( x \) be the common multiplier. A's age is represented as \( 3x \) and B's age as \( 5x \). The sum is calculated as: \[ 3x + 5x = 40 \Rightarrow 8x = 40 \Rightarrow x = 5 \]

4. Determining B's Age:

B's age is: \[ 5x = 5 \times 5 = 25 \]

Conclusion:

B's age is 25 years.