The ratio of present ages of a woman and a man is 5 : 4 . 4 years ago. the man's age was 28 years. What will be woman's age after 6 years ?

Options

A. 42 years
B. 40year
C. 45 years
D. 46years

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Define the present ages based on the ratio
Let the present age of the woman be \(5x\) and the present age of the man be \(4x\), where \(x\) is a common multiplier.

### Step 2: Use the information about the man's age 4 years ago
According to the problem, 4 years ago, the man's age was 28 years. Therefore, we can write the equation:
\[ 4x - 4 = 28 \]

### Step 3: Solve for \(x\)
Now, we will solve the equation for \(x\):
\[ 4x - 4 = 28 \\ 4x = 28 + 4 \\ 4x = 32 \\ x = \frac{32}{4} \\ x = 8 \]

### Step 4: Find the present age of the woman
Now that we have the value of \(x\), we can find the present age of the woman:
\[ \text{Present age of the woman} = 5x = 5 \times 8 = 40 \text{ years} \]

### Step 5: Calculate the woman's age after 6 years
To find the woman's age after 6 years, we add 6 to her present age:
\[ \text{Age after 6 years} = 40 + 6 = 46 \text{ years} \]

### Final Answer
The woman's age after 6 years will be **46 years**.

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