For every set of 19 kites sold, a vendor gives 1 kite extra, free of cost. In order to give a discount of 10% the number of extra kites he should give in a sale of 27 kites to the nearest integer is –

Options

A. 3
B. 5
C. 7
D. 9

Answer

To solve the problem, we need to determine how many extra kites the vendor should give in order to provide a 10% discount when selling 27 kites. Let's break it down step by step.

### Step 1: Understand the discount
The vendor wants to give a 10% discount on the sale of 27 kites. This means that the customer should effectively receive 90% of the total value of the kites.

### Step 2: Calculate the value of 27 kites
If we consider the value of 27 kites as 100%, then the value after a 10% discount would be:
\[ \text{Value after discount} = 27 \text{ kites} \times 90\% = 27 \times 0.9 = 24.3 \text{ kites} \]

### Step 3: Determine the number of extra kites needed
To find out how many extra kites need to be given to achieve this discount, we need to find out how many kites would effectively make the customer feel they are getting more value.

If the vendor gives extra kites, the total number of kites the customer receives increases. We need to find out how many extra kites (let's denote this as \( x \)) should be given such that:
\[ 27 + x = 24.3 \]

### Step 4: Solve for \( x \)
To find \( x \):
\[ x = 24.3 - 27 \]
\[ x = -2.7 \]

Since we cannot have a negative number of kites, we need to interpret this differently. The vendor gives 1 extra kite for every 19 kites sold.

### Step 5: Calculate the equivalent discount in terms of kites
From the previous understanding, we know that for every 19 kites sold, 1 kite is given for free. Thus, to find out how many extra kites correspond to a 10% discount on 27 kites, we can use the ratio:
- 10% of 27 kites corresponds to:
\[ 10\% \text{ of } 27 = 2.7 \text{ kites} \]

### Step 6: Round to the nearest integer
Since we need to give a whole number of kites, we round 2.7 to the nearest integer, which is 3.

### Conclusion
The vendor should give 3 extra kites to provide a 10% discount when selling 27 kites.

### Final Answer
The number of extra kites he should give is **3**.

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