At a charity show the price of each ticket was Rs `32 1/2` The total amount collected by a boy 2 was Rs `877 1/2`. How many tickets were sold by him?

Answer

To find out how many tickets were sold by the boy at the charity show, we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
The price of each ticket is given as Rs. \(32 \frac{1}{2}\). We can convert this mixed number to an improper fraction:
\[ 32 \frac{1}{2} = \frac{(32 \times 2) + 1}{2} = \frac{64 + 1}{2} = \frac{65}{2} \]

### Step 2: Convert Total Amount Collected to Improper Fraction
The total amount collected is given as Rs. \(877 \frac{1}{2}\). We convert this mixed number to an improper fraction:
\[ 877 \frac{1}{2} = \frac{(877 \times 2) + 1}{2} = \frac{1754 + 1}{2} = \frac{1755}{2} \]

### Step 3: Set Up the Equation for Number of Tickets Sold
To find the number of tickets sold, we will divide the total amount collected by the price of one ticket:
\[ \text{Number of tickets sold} = \frac{\text{Total Amount Collected}}{\text{Price of One Ticket}} = \frac{\frac{1755}{2}}{\frac{65}{2}} \]

### Step 4: Simplify the Division of Fractions
When dividing fractions, we multiply by the reciprocal:
\[ \frac{1755}{2} \div \frac{65}{2} = \frac{1755}{2} \times \frac{2}{65} \]
The \(2\) in the numerator and denominator cancels out:
\[ = \frac{1755}{65} \]

### Step 5: Perform the Division
Now we need to divide \(1755\) by \(65\):
\[ 1755 \div 65 = 27 \]

### Conclusion
Thus, the number of tickets sold by the boy is \(27\).

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