Question

If the ratio of the ages of A and B is 4:5, and the sum of their ages is 72 years, what is B's age?

• A. 36
• B. 40
• C. 32
• D. 30

Hint:

For ratio problems, always assign variables and write equations based on sums or differences to solve for unknowns.

Answer 1

The Correct Option is B

Step 1: Let the ages of A and B be \(4x\) and \(5x\) respectively, based on the given ratio.
Step 2: According to the problem, the sum of their ages is 72:
\[ 4x + 5x = 72 \] Step 3: Combine like terms:
\[ 9x = 72 \] Step 4: Solve for \(x\):
\[ x = \frac{72}{9} = 8 \] Step 5: Calculate B's age by multiplying \(x\) by 5:
\[ 5 \times 8 = 40 \] Hence, B's age is 40 years.