Ratio of present ages of Pankaj and Punit is 5 : 6 and the sum of their ages is 33 years. What will be difference (in years) of their ages?

Options

A. 2
B. 3
C. 4
D. 5

Explanation

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

### Step 1: Understand the ratio of ages
The ratio of the present ages of Pankaj and Punit is given as 5:6. This means if we let Pankaj's age be 5x and Punit's age be 6x, where x is a common multiplier.

**Hint:** Remember that in a ratio, the parts can be represented as multiples of a variable.

### Step 2: Set up the equation for the sum of their ages
According to the problem, the sum of their ages is 33 years. Therefore, we can write the equation:
\[ 5x + 6x = 33 \]

**Hint:** Combine the terms on the left side to simplify the equation.

### Step 3: Solve for x
Combine the terms:
\[ 11x = 33 \]
Now, divide both sides by 11 to find the value of x:
\[ x = \frac{33}{11} = 3 \]

**Hint:** When solving for x, make sure to perform the division correctly.

### Step 4: Calculate the ages of Pankaj and Punit
Now that we have the value of x, we can find the actual ages:
- Pankaj's age = \( 5x = 5 \times 3 = 15 \) years
- Punit's age = \( 6x = 6 \times 3 = 18 \) years

**Hint:** Substitute the value of x back into the expressions for their ages.

### Step 5: Find the difference in their ages
Now, we can find the difference between their ages:
\[ \text{Difference} = \text{Punit's age} - \text{Pankaj's age} = 18 - 15 = 3 \text{ years} \]

**Hint:** Remember that the difference can be found by subtracting the smaller age from the larger age.

### Final Answer
The difference in their ages is 3 years.

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