Understanding and Solving Unitary Method Questions: A Comprehensive Guide

The unitary method is a fundamental technique in mathematics used to find the value of a single unit from a given quantity. This method is particularly useful in solving problems related to pricing, speed, and other proportional relationships. In this article, we will demonstrate how to use the unitary method to solve a specific problem: if 20 apples cost 185 rupees, how much would 7 apples cost?

Step-by-Step Guide

To solve the problem using the unitary method, follow these steps:

Find the cost of one apple:

Given that 20 apples cost 185 rupees, you can calculate the cost of one apple by dividing the total cost by the number of apples.

Cost of one apple Total cost / Number of apples

Cost of one apple 185 rupees / 20

Cost of one apple 9.25 rupees

Find the cost of 7 apples:

Now that you know the cost of one apple, simply multiply it by the number of apples you want (7 apples).

Cost of 7 apples Cost of one apple × 7

Cost of 7 apples 9.25 rupees × 7

Cost of 7 apples 64.75 rupees

Therefore, the cost of 7 apples is 64.75 rupees.

Example and Explanation

Consider another example to illustrate the unitary method clearly. Suppose you have 10 chocolates for Rs 20. What is the cost of 1 chocolate?

Cost of one chocolate Total cost / Number of chocolates

Cost of one chocolate 20 rupees / 10

Cost of one chocolate 2 rupees

Now, what is the cost of 7 chocolates?

Cost of 7 chocolates Cost of one chocolate × 7

Cost of 7 chocolates 2 rupees × 7

Cost of 7 chocolates 14 rupees

This example simplifies the process of finding the unit price and then multiplying it by the desired quantity.

Conclusion

The unitary method is a powerful tool for solving problems involving proportional relationships. By breaking down the problem into smaller, manageable units, you can easily find the value of a single unit and then scale it up or down as needed. In the given example, we calculated the cost of 7 apples based on the cost of 20 apples, demonstrating the straightforward nature of the unitary method.

To summarize, the unitary method is simply a logical approach to solving problems where you need to find the value of a single unit and then apply it to the desired quantity. The steps are:

Find the value of one unit (in this case, one apple).Multiply the value of one unit by the required quantity.

With practice, solving such problems becomes second nature. The key is to understand the underlying principle and apply it consistently.