The Problem:

The problem states that the perimeter of a rectangle is 240 cm. When the length of the rectangle is decreased by 10% and the breadth is increased by 20%, the new rectangle has the same perimeter. We need to find the length and breadth of the original rectangle.

Understanding the Problem:

To solve this problem, we need to understand the concept of perimeter and how it relates to the dimensions of a rectangle. The perimeter of a rectangle is the sum of all its sides. In this case, we are given that the perimeter is 240 cm.

Let's solve the problem step by step:

Step 1: Representing the dimensions of the rectangle:

Let's assume the original length of the rectangle is L and the original breadth is B. We are given that the perimeter of the rectangle is 240 cm.

Step 2: Calculating the initial perimeter:

The initial perimeter of the rectangle can be calculated using the formula: P = 2L + 2B, where P is the perimeter, L is the length, and B is the breadth.

Given that the perimeter is 240 cm, we have the equation: 2L + 2B = 240.

Step 3: Modifying the dimensions of the rectangle:

According to the problem, the length of the rectangle is decreased by 10% and the breadth is increased by 20%.

To decrease the length by 10%, we can multiply L by (100% - 10%) = 90% or 0.9.

To increase the breadth by 20%, we can multiply B by (100% + 20%) = 120% or 1.2.

So, the new length is 0.9L and the new breadth is 1.2B.

Step 4: Calculating the new perimeter:

The new perimeter of the modified rectangle can be calculated using the same formula: P = 2(0.9L) + 2(1.2B).

Since the new perimeter is equal to the original perimeter, we have the equation: 2(0.9L) + 2(1.2B) = 240.

Step 5: Solving the equation:

Let's solve the equation to find the values of L and B.

Expanding the equation, we get: 1.8L + 2.4B = 240.

Rearranging the terms, we have: 1.8L = 240 - 2.4B.

Dividing both sides by 1.8, we get: L = (240 - 2.4B)/1.8.

Step 6: Substituting the value of L:

Substituting the value of L in the equation 2L + 2B = 240, we get: 2((240 - 2.4B)/1.8) + 2B = 240.

Simplifying the equation, we have: (480 - 4.8B)/1.8 + 2B = 240.

Multiplying both sides by 1.8 to eliminate the denominator, we get: 480 - 4.8B + 3.6B = 432