Amit buys chocolates worth Rs. `97 (1)/(2)`. If one chocolate costs Rs. `9 (3)/(4)`, how many chocolates did he buy?

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Convert the mixed numbers to improper fractions
First, we need to convert the total cost of chocolates and the cost of one chocolate from mixed numbers to improper fractions.

1. **Total cost of chocolates**:
- Given: Rs. \(97 \frac{1}{2}\)
- Convert to improper fraction:
\[ 97 \frac{1}{2} = \frac{97 \times 2 + 1}{2} = \frac{194 + 1}{2} = \frac{195}{2} \]

2. **Cost of one chocolate**:
- Given: Rs. \(9 \frac{3}{4}\)
- Convert to improper fraction:
\[ 9 \frac{3}{4} = \frac{9 \times 4 + 3}{4} = \frac{36 + 3}{4} = \frac{39}{4} \]

### Step 2: Set up the equation to find the number of chocolates
To find the number of chocolates, we divide the total cost by the cost of one chocolate:
\[ \text{Number of chocolates} = \frac{\text{Total cost}}{\text{Cost of one chocolate}} = \frac{\frac{195}{2}}{\frac{39}{4}} \]

### Step 3: Simplify the division of fractions
When dividing fractions, we multiply by the reciprocal of the second fraction:
\[ \frac{195}{2} \div \frac{39}{4} = \frac{195}{2} \times \frac{4}{39} \]

### Step 4: Multiply the fractions
Now we can multiply the fractions:
\[ = \frac{195 \times 4}{2 \times 39} \]

### Step 5: Simplify the expression
1. Simplify \(2\) and \(4\):
\[ = \frac{195 \times 2}{39} \]
2. Now, simplify \(195\) and \(39\):
\[ 39 \text{ goes into } 195 \text{ exactly } 5 \text{ times (since } 39 \times 5 = 195\text{)} \]
So we have:
\[ = \frac{5 \times 2}{1} = 10 \]

### Conclusion
Thus, the number of chocolates Amit bought is **10**.

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