The ratio of three numbers is 2 : 3 : 5. If the sum of the three numbers is 275, then what is the largest among these three numbers?

Introduction / Context:
This is a direct ratio problem involving three numbers. We know their ratio and their total sum, and we need to find the largest number. Such questions test whether a student can convert a ratio into actual values when the sum is given. It is a standard topic in ratio and proportion in quantitative aptitude sections.

Given Data / Assumptions:

• Three numbers are in the ratio 2 : 3 : 5.
• The sum of the three numbers is 275.
• We need to find the largest of the three numbers.
• The numbers can be fractional because the total is not necessarily a multiple of the total ratio sum.

Concept / Approach:
When numbers are in a ratio, we can assume them to be 2k, 3k and 5k for some common multiplier k. The sum then becomes 2k + 3k + 5k, which must equal the given total 275. Solving this simple linear equation gives k, and then each number is calculated by multiplying the ratio part by k. The largest number corresponds to the largest ratio term.

Step-by-Step Solution:

Verification / Alternative check:
Add the three computed numbers: 55 + 82.5 + 137.5 = 275, which matches the given total. Also, the ratio 55 : 82.5 : 137.5 simplifies to 2 : 3 : 5 if we divide each term by 27.5. This double check confirms that the calculations and the largest number are correct.

Why Other Options Are Wrong:

• 142, 110.5 and 82.5 do not correspond to 5k when k = 27.5.
• 82.5 is actually the middle number, not the largest one.
• Values like 142 and 110.5 break the ratio 2 : 3 : 5 when combined with the other two implied numbers.

Common Pitfalls:
A typical mistake is to think that all three numbers must be integers and reject fractional values, which is not necessary in ratio problems unless the question explicitly restricts them. Another error is to miscalculate the sum of ratio terms or to assign k incorrectly, leading to wrong final values. Careful arithmetic in forming and solving the equation 10k = 275 avoids these issues.

Final Answer:
The largest of the three numbers is 137.5.