The ratio of two numbers are 3 : 5 and the addition of those numbers is 240, what is the difference of those numbers ?

Question

Accepted Answer

To solve the problem, we need to find the difference between two numbers given their ratio and sum. The ratio of the two numbers is 3:5, and their sum is 240.

Let's denote the two numbers as 3x and 5x, where x is a common multiplier.

1. **Calculate the sum of the numbers:**

According to the problem, the sum of the numbers is 240.

$$
   3x + 5x = 240
   $$

$$
   8x = 240
   $$

Solving for x, we divide both sides by 8:

$$
   x = \frac{240}{8} = 30
   $$

2. **Find the actual numbers:**

Now that we have x, we can find the actual numbers:

- The first number is $3x = 3 \times 30 = 90$.
   - The second number is $5x = 5 \times 30 = 150$.

3. **Calculate the difference between the numbers:**

The difference between the two numbers is:

$$
   150 - 90 = 60
   $$

Therefore, the difference between the two numbers is 60, which corresponds to Option 1.

**Explanation for why other options are incorrect:**

- **Option 2 (100):** This would imply a larger difference than calculated. Given the numbers 90 and 150, the difference is clearly 60, not 100.
  
- **Option 3 (120):** This would imply an even larger difference, which is not possible given the numbers derived from the ratio and sum.

- **Option 4 (90):** This suggests a difference that is larger than the actual difference of 60. The calculation clearly shows the difference is 60.

Thus, Option 1 is the correct answer, as it accurately reflects the difference between the two numbers based on the given ratio and sum.