Dividing 108 in the ratio 4:5

To divide 108 in the ratio 4:5, we need to find two numbers that add up to 108 and are in the ratio 4:5. Let's solve this step by step.

Finding the parts

Step 1: Let's assume the two parts are 4x and 5x, where x is a common factor.

Step 2: According to the ratio, 4x + 5x = 108.

Step 3: Simplifying the equation, we get 9x = 108.

Step 4: Dividing both sides by 9, we find x = 12.

Step 5: Now, substituting the value of x back into the parts, we get the two parts as 4x = 4(12) = 48 and 5x = 5(12) = 60.

Verifying the ratio

To verify that the two parts are indeed in the ratio 4:5, we divide the larger part by the smaller part.

60 / 48 = 1.25

The ratio 60:48 simplifies to 5:4, which is the same as the given ratio 4:5. Therefore, the answer is option 'A' 48 and 60.

Explanation in detail:

- Given: The number 108 needs to be divided into two parts in the ratio 4:5.
- Assumption: Let the two parts be 4x and 5x, where x is a common factor.
- Equation: According to the ratio, 4x + 5x = 108.
- Simplifying the equation: 9x = 108.
- Solving for x: Dividing both sides by 9, x = 12.
- Finding the parts: Substituting the value of x back into the parts, we get 4x = 4(12) = 48 and 5x = 5(12) = 60.
- Verifying the ratio: Dividing the larger part by the smaller part, 60 / 48 = 1.25. The ratio 60:48 simplifies to 5:4, which is the same as the given ratio 4:5.
- Conclusion: Therefore, the correct answer is option 'A' 48 and 60.