Quantity I . Sum of present ages of Shivam and Preashant is 32 years and Shivam is 8 years older than Prashant . Find present age of Prashant
Quantity II. 15 years

Options

A. If Quantity I ` gt` Quantity II
B. If Quantity I ` lt` Quantity II
C. If Quantity I ` ge` Quantity II
D. If Quantity I ` le` Quantity II

Answer

To solve the problem step by step, we will follow the information given in the question and set up the equations accordingly.

### Step 1: Define the Variables
Let the present age of Prashant be \( x \) years.

**Hint:** Start by defining the unknown variable for the age you need to find.

### Step 2: Express Shivam's Age
Since Shivam is 8 years older than Prashant, we can express Shivam's age as:
\[ \text{Shivam's age} = x + 8 \]

**Hint:** Use the relationship given in the problem to express one variable in terms of another.

### Step 3: Set Up the Equation
According to the problem, the sum of their ages is 32 years. Therefore, we can write the equation:
\[ x + (x + 8) = 32 \]

**Hint:** Combine the expressions for their ages to form an equation based on the total given.

### Step 4: Simplify the Equation
Now, simplify the equation:
\[ 2x + 8 = 32 \]

**Hint:** Combine like terms and isolate the variable on one side of the equation.

### Step 5: Solve for \( x \)
Subtract 8 from both sides:
\[ 2x = 32 - 8 \]
\[ 2x = 24 \]

Now, divide by 2:
\[ x = 12 \]

**Hint:** Perform arithmetic operations carefully to isolate the variable and find its value.

### Step 6: Conclusion
The present age of Prashant is \( 12 \) years.

### Step 7: Compare with Quantity II
Now, we compare Quantity I (Prashant's age, which is 12 years) with Quantity II (15 years):
- Quantity I: 12 years
- Quantity II: 15 years

Since \( 12 < 15 \), we conclude that Quantity I is less than Quantity II.

**Final Answer:** Quantity I is less than Quantity II.