Calculating Pizza Cost: Step-by-Step Solution

Let's break down how to find the cost of a portion of a pizza when the cost of another portion is known. The question tells us the cost of 2/3rd of a pizza and asks for the cost of 3/5th of the same pizza.

Step 1: Find the Cost of the Full Pizza

We are given that the cost of \(\frac{2}{3}\) of the pizza is Rs. 300.

If \(\frac{2}{3}\) of the pizza costs Rs. 300, then to find the cost of the whole pizza (which is 1 or \(\frac{3}{3}\) of the pizza), we can set up a proportion or think about it logically:

• If 2 parts out of 3 cost Rs. 300, then 1 part costs Rs. \(300 \div 2 = \text{Rs. } 150\).
• The whole pizza is 3 parts. So, the cost of the whole pizza is \(3 \times \text{Rs. } 150 = \text{Rs. } 450\).

Alternatively, using a direct calculation:

Cost of 1 pizza = Cost of \(\frac{2}{3}\) pizza \(\div \frac{2}{3}\)

Cost of 1 pizza = Rs. \(300 \div \frac{2}{3}\)

Cost of 1 pizza = Rs. \(300 \times \frac{3}{2}\)

Cost of 1 pizza = Rs. \(\frac{900}{2}\)

Cost of 1 pizza = Rs. 450

So, the full pizza costs Rs. 450.

Step 2: Calculate the Cost of 3/5th of the Pizza

Now that we know the cost of the whole pizza is Rs. 450, we can find the cost of \(\frac{3}{5}\) of the pizza.

Cost of \(\frac{3}{5}\) pizza = Cost of 1 pizza \(\times \frac{3}{5}\)

Cost of \(\frac{3}{5}\) pizza = Rs. \(450 \times \frac{3}{5}\)

Cost of \(\frac{3}{5}\) pizza = Rs. \(\frac{450 \times 3}{5}\)

We can simplify the calculation by dividing 450 by 5 first:

\(450 \div 5 = 90\)

Now, multiply by 3:

Cost of \(\frac{3}{5}\) pizza = Rs. \(90 \times 3\)

Cost of \(\frac{3}{5}\) pizza = Rs. 270

Thus, 3/5th of the pizza will cost Rs. 270.

Comparing with the Options

Let's check our calculated cost against the given options:

• Option 1: Rs. 180
• Option 2: Rs. 250
• Option 3: Rs. 225
• Option 4: Rs. 270

Our calculated cost, Rs. 270, matches Option 4.

Final Answer Derivation

By first determining the total cost of the pizza based on the price of 2/3rd of it, and then calculating 3/5th of that total cost, we arrived at the final cost. The calculation confirms that if 2/3rd of a pizza costs Rs. 300, then 3/5th of the same pizza will cost Rs. 270.

Revision Table: Pizza Cost Calculation

Additional Information: Understanding Fractions and Proportions

This problem involves working with fractions and understanding proportions. A fraction represents a part of a whole. In this case, \(\frac{2}{3}\) and \(\frac{3}{5}\) represent portions of the total pizza.

• Unitary Method: A common way to solve such problems is using the unitary method. Find the cost of the unit (the whole pizza in this case) first, and then use that to find the cost of the desired portion.
• Proportionality: The cost of a portion of the pizza is directly proportional to the size of the portion. If you double the portion size, the cost doubles. If you halve it, the cost halves. This principle allows us to find the cost of the whole pizza from a known portion cost and then calculate the cost of another portion.
• Fraction Multiplication: To find a fraction of a number (like \(\frac{3}{5}\) of Rs. 450), you multiply the fraction by the number.

Practicing problems involving fractions of quantities helps in understanding how to apply these concepts in everyday situations, like calculating costs based on portions.