The Cost of 12 identical articles is Rs.1,080. How many articles can one buy for Rs.1,620?

The Cost of 12 identical articles is Rs.1,080. How many articles can one buy for Rs.1,620?

The problem establishes a direct relationship between the amount spent and the number of articles bought, which means the amount is proportional to the number of articles.

Using the Proportionality Formula:

We can use the proportionality formula to solve the problem: x1/y1 = x2/y2,

where

x1 is the initial amount,

y1 is the initial number of articles,

x2 is the new amount, and

y2 is the new number of articles

Initial amount x1 = Rs. 1,080 (cost of 12 identical articles)

Initial number of articles y1 = 12

New amount x2 = Rs. 1,620

We need to find the new number of articles y2

Substitute the given values into the proportionality formula

12/1080 = x2/1620

Therefore x2 = 18

For Rs. 1,620, one can buy 18 identical articles.

Cost and Quantity Relationship

There is a direct relationship between the cost of items and the quantity that can be purchased with a given amount of money. As the amount of money spent increases, the number of items that can be bought also increases, assuming the price per item remains constant.

Using Proportionality:

• Proportionality is a concept used to express the relationship between two quantities that change together.
• In the context of buying articles, the amount spent is proportional to the number of articles bought.

Proportional Formula:

• The proportional formula states that the ratio of the initial amount and quantity is equal to the ratio of the new amount and quantity.
• This formula helps in calculating the new quantity based on changes in the amount spent or price per item.

Calculation Process:

• To calculate the number of articles that can be bought for a given amount, you set up a proportion using the initial amount, initial quantity, new amount, and unknown new quantity.
• Cross-multiply and solve for the unknown quantity to determine how many articles can be purchased with the new amount.

Applications:

• Understanding this concept is practical for budgeting, shopping decisions, and business calculations.
• It helps consumers and businesses make informed choices based on budget constraints and pricing information.