After 6 years Pradhan’s age will be `3/7` times the age of his father. 10 years ago the ratio in the age of Pradhan and his father was 1 : 5. What is the present age of Pradhan’s father ?

Options

A. 40 years
B. 50 years
C. 56 years
D. Data is inadequate

Answer

To solve the problem, we will break it down into steps.

### Step 1: Define Variables
Let Pradhan's present age be \( x \). Since the ratio of their ages 10 years ago was 1:5, we can express his father's present age as \( 5x \).

### Step 2: Set Up Equations
From the problem, we know:
- 10 years ago, Pradhan's age was \( x - 10 \).
- 10 years ago, his father's age was \( 5x - 10 \).

According to the problem, the ratio of their ages 10 years ago is:
\[ \frac{x - 10}{5x - 10} = \frac{1}{5} \]

### Step 3: Cross Multiply to Solve for x
Cross multiplying gives us:
\[ 5(x - 10) = 1(5x - 10) \]
Expanding both sides:
\[ 5x - 50 = 5x - 10 \]

### Step 4: Simplify the Equation
Subtract \( 5x \) from both sides:
\[ -50 = -10 \]
This indicates that our equation is consistent, but we need to find the present ages.

### Step 5: Set Up the Second Equation
Now, according to the problem, after 6 years, Pradhan's age will be \( x + 6 \) and his father's age will be \( 5x + 6 \). The relationship given is:
\[ x + 6 = \frac{3}{7}(5x + 6) \]

### Step 6: Cross Multiply Again
Cross multiplying gives:
\[ 7(x + 6) = 3(5x + 6) \]
Expanding both sides:
\[ 7x + 42 = 15x + 18 \]

### Step 7: Rearranging the Equation
Rearranging gives:
\[ 7x - 15x = 18 - 42 \]
\[ -8x = -24 \]
Dividing both sides by -8:
\[ x = 3 \]

### Step 8: Find Present Age of Pradhan's Father
Now that we have Pradhan's age, we can find his father's age:
\[ \text{Father's age} = 5x = 5 \times 3 = 15 \]

### Step 9: Calculate Present Age
Since we need the present age, we add 10 years (as per the original problem statement):
\[ \text{Present age of Pradhan's father} = 15 + 10 = 25 \]

### Final Answer
The present age of Pradhan's father is **25 years**.

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