The ratio of the present ages of A and B is `1 : 3`. After 10 years, the ratio of their ages will be `2 : 5`. Find B's present age.

Options

A. A)70 years
B. B)85 years
C. C)90 years
D. D)80 years

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the present ages of A and B
Let the present age of A be \( x \) years. According to the problem, the present age of B is \( 3x \) years since the ratio of their ages is \( 1:3 \).

### Step 2: Set up the equation for their ages after 10 years
After 10 years, the age of A will be \( x + 10 \) and the age of B will be \( 3x + 10 \). The problem states that the ratio of their ages after 10 years will be \( 2:5 \).

### Step 3: Write the equation based on the future age ratio
We can set up the equation based on the future ratio:
\[ \frac{x + 10}{3x + 10} = \frac{2}{5} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 5(x + 10) = 2(3x + 10) \]

### Step 5: Expand both sides
Expanding both sides, we get:
\[ 5x + 50 = 6x + 20 \]

### Step 6: Rearrange the equation to solve for x
Now, we will rearrange the equation to isolate \( x \):
\[ 50 - 20 = 6x - 5x \]
\[ 30 = x \]

### Step 7: Find B's present age
Since \( x \) represents A's present age, we can find B's present age:
\[ \text{B's present age} = 3x = 3 \times 30 = 90 \text{ years} \]

### Final Answer
B's present age is **90 years**.

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