Arpit played for `2(3)/(7)` of an hour and Pulkit played for `2(4)/(9)` of an hour. Who played for less time ?

Answer

To determine who played for less time between Arpit and Pulkit, we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

**For Arpit:**
- Arpit played for \(2 \frac{3}{7}\) hours.
- To convert this to an improper fraction:
\[ \text{Improper fraction} = (2 \times 7 + 3) / 7 = (14 + 3) / 7 = \frac{17}{7} \]

**For Pulkit:**
- Pulkit played for \(2 \frac{4}{9}\) hours.
- To convert this to an improper fraction:
\[ \text{Improper fraction} = (2 \times 9 + 4) / 9 = (18 + 4) / 9 = \frac{22}{9} \]

### Step 2: Compare the Two Improper Fractions
Now, we have:
- Arpit's time: \(\frac{17}{7}\)
- Pulkit's time: \(\frac{22}{9}\)

To compare these fractions, we need a common denominator. The least common multiple (LCM) of 7 and 9 is 63.

### Step 3: Convert to a Common Denominator
Next, we will convert both fractions to have the same denominator of 63.

**For Arpit:**
\[ \frac{17}{7} = \frac{17 \times 9}{7 \times 9} = \frac{153}{63} \]

**For Pulkit:**
\[ \frac{22}{9} = \frac{22 \times 7}{9 \times 7} = \frac{154}{63} \]

### Step 4: Compare the Numerators
Now we can compare the two fractions:
- Arpit: \(\frac{153}{63}\)
- Pulkit: \(\frac{154}{63}\)

Since \(153 < 154\), it follows that:
\[ \frac{153}{63} < \frac{154}{63} \]

### Conclusion
Thus, Arpit played for less time than Pulkit.

**Final Answer:**
Arpit played for less time.

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