The ratio of the age of A and B 25 years ago was 3 : 8. The ratio of their present ages is 8 : 13. What will be the present age (in years) of B?

Options

A. A)15
B. B)40
C. C)65
D. D)50

Answer

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

### Step 1: Understand the Ratios
We are given two ratios:
1. The ratio of ages of A and B 25 years ago was 3:8.
2. The ratio of their present ages is 8:13.

### Step 2: Set Up the Equations
Let the ages of A and B 25 years ago be represented as:
- Age of A = 3x (for some value x)
- Age of B = 8x

Since these ages were 25 years ago, we can express their present ages as:
- Present age of A = 3x + 25
- Present age of B = 8x + 25

### Step 3: Present Age Ratio
We know that the present age ratio of A and B is 8:13. Therefore, we can set up the equation:
\[ \frac{3x + 25}{8x + 25} = \frac{8}{13} \]

### Step 4: Cross-Multiply to Solve for x
Cross-multiplying gives us:
\[ 13(3x + 25) = 8(8x + 25) \]
Expanding both sides:
\[ 39x + 325 = 64x + 200 \]

### Step 5: Rearranging the Equation
Now, rearranging the equation to isolate x:
\[ 39x - 64x = 200 - 325 \]
\[ -25x = -125 \]
\[ x = 5 \]

### Step 6: Finding Present Ages
Now that we have the value of x, we can find the present ages of A and B:
- Present age of A = 3x + 25 = 3(5) + 25 = 15 + 25 = 40 years
- Present age of B = 8x + 25 = 8(5) + 25 = 40 + 25 = 65 years

### Step 7: Conclusion
Thus, the present age of B is **65 years**.

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