The ratio of two numbers is 3 : 4 and sum of these two numbers is 420, then greater number is

Question

Accepted Answer

To determine the greater number when the ratio of two numbers is 3:4 and their sum is 420, we can use the following logical steps:

1. **Understanding the Ratio**: The ratio 3:4 implies that for every 3 parts of the first number, there are 4 parts of the second number. Let's denote the first number as 3x and the second number as 4x, where x is a common multiplier.

2. **Setting Up the Equation**: According to the problem, the sum of these two numbers is 420. Therefore, we can set up the equation:
   $$
   3x + 4x = 420
   $$

3. **Solving for x**: Simplify the equation:
   $$
   7x = 420
   $$
   Divide both sides by 7 to solve for x:
   $$
   x = \frac{420}{7} = 60
   $$

4. **Finding the Numbers**: Now that we have x, we can find the actual numbers:
   - The first number (3x) is:
     $$
     3 \times 60 = 180
     $$
   - The second number (4x) is:
     $$
     4 \times 60 = 240
     $$

5. **Identifying the Greater Number**: Between 180 and 240, the greater number is 240.

6. **Conclusion**: Therefore, the greater number is 240, which corresponds to Option 3.

**Explanation for Incorrect Options**:

- **Option 1 (175)**: This option is incorrect because, based on the ratio and sum provided, the calculations do not yield 175 as either of the numbers. The numbers calculated are 180 and 240.

- **Option 2 (200)**: This option is incorrect because 200 does not fit the ratio of 3:4 when the sum is 420. The correct numbers are 180 and 240.

- **Option 4 (315)**: This option is incorrect because 315 exceeds the sum of 420 when combined with any other number in the ratio 3:4. The correct numbers are 180 and 240.

Thus, the correct answer is Option 3, which is 240.