Problem 1:
Question: Find the area of a circle with radius 7 cm.
Solution:
The formula for the area of a circle is:
```
A = πr²
```
Where:
A = Area of the circle
r = Radius of the circle
Substituting the given value of radius (r = 7 cm) into the formula, we get:
```
A = (22/7) × 7²
A = (22/7) × 49
A = 154 cm²
```
Therefore, the area of the circle is 154 cm².
Problem 2:
Question: A rectangular garden has a length of 15 m and a width of 10 m. Find the perimeter of the garden.
Solution:
The formula for the perimeter of a rectangle is:
```
P = 2 (l + w)
```
Where:
P = Perimeter of the rectangle
l = Length of the rectangle
w = Width of the rectangle
Substituting the given values of length (l = 15 m) and width (w = 10 m) into the formula, we get:
```
P = 2 (15 + 10)
P = 2 (25)
P = 50 m
```
Therefore, the perimeter of the rectangular garden is 50 m.
Problem 3:
Question: A shopkeeper buys 100 oranges at a cost of Rs. 20 each. He sells 80 oranges at a profit of Rs. 5 each. If he wants to make an overall profit of 10%, how much should he sell the remaining oranges for?
Solution:
Step 1: Calculate the total cost of purchasing 100 oranges.
Cost price of 1 orange = Rs. 20
Total cost price of 100 oranges = 100 × 20 = Rs. 2000
Step 2: Calculate the selling price of 80 oranges.
Selling price of 1 orange with a profit of Rs. 5 = Rs. (20 + 5) = Rs. 25
Selling price of 80 oranges = 80 × 25 = Rs. 2000
Step 3: Calculate the profit made from selling 80 oranges.
Profit = Selling price - Cost price
Profit from selling 80 oranges = Rs. 2000 - Rs. 2000 = Rs. 0
Step 4: Calculate the overall profit he wants to make.
Overall profit = 10% of total cost price
Overall profit = (10/100) × 2000 = Rs. 200
Step 5: Calculate the selling price of the remaining oranges to achieve the desired overall profit.
Amount to be recovered from the sale of remaining oranges (20 oranges) = Total desired profit - Profit made from selling 80 oranges
Amount to be recovered = Rs. 200 - Rs. 0 = Rs. 200
Selling price of 1 orange to achieve the desired overall profit = Rs. (200 / 20) = Rs. 10
Therefore, the shopkeeper should sell the remaining 20 oranges for Rs. 10 each to achieve an overall profit of 10%.