In this numerical analogy question, select the related number from the given alternatives to complete the proportion: 60 : 15 :: 100 : ?

Introduction / Context:
This numerical analogy problem tests a very common operation involving fractions and division. You are given the pair 60 and 15 and asked to find the number that should correspond to 100 in the same way. Such questions are standard in quantitative aptitude tests and check whether you can recognise simple fractional relationships and apply them consistently to new numbers.

Given Data / Assumptions:
The first pair is 60 and 15.
The second pair starts with 100, and we must determine the missing number.
The options available are 45, 35, 5, 25, and 50.
We assume that whatever operation transforms 60 into 15 must be applied to 100 to obtain the correct answer.

Concept / Approach:
To relate 60 and 15, we can test simple arithmetic operations. Dividing 60 by 4 gives 15, because 60 / 4 = 15. Expressed as a fraction, 15 is one quarter of 60. This suggests that the transformation is division by 4. If that is correct, then 100 must also be divided by 4 to find the corresponding term. Recognising quarter, half, or other simple fractional relationships is essential for solving these analogies quickly.

Step-by-Step Solution:
Step 1: Check the ratio between 60 and 15. Compute 60 / 15 = 4.Step 2: This means that 15 is equal to 60 divided by 4, or one quarter of 60.Step 3: Apply the same operation to the second number 100. Compute 100 / 4.Step 4: We know that 100 / 4 = 25.Step 5: Confirm that 25 is present among the options and recognise it as the only value that follows the same divide by 4 pattern.

Verification / Alternative check:
We can also examine the relationship using proportions. If 60 : 15 :: 100 : x, then 60 / 15 = 100 / x. Since 60 / 15 = 4, we have 4 = 100 / x, which implies x = 100 / 4 = 25. This matches the result obtained from direct division. Another way to see it is that 25 is one quarter of 100, just as 15 is one quarter of 60, so the analogy is consistent.

Why Other Options Are Wrong:
Option 45 is 3 less than 48, which would be 60 multiplied by a certain factor, but it does not represent one quarter of 100.
Option 35 is not a simple fraction such as one half or one quarter of 100, so it does not match the operation seen in the first pair.
Option 5 is too small and would correspond to dividing 100 by 20, which is completely different from dividing 60 by 4.
Option 50 is half of 100, which is not the same as being one quarter, so it does not align with the relation between 60 and 15.

Common Pitfalls:
Some candidates might hurriedly choose 50 because they notice that 15 is less than 60 and think in terms of halves instead of quarters. Others may try to match approximate differences (like subtracting a constant) without confirming the exact operation. The safest approach is to calculate the precise ratio or fraction between the first pair and then apply it directly to the second number, ensuring consistency with the provided options.

Final Answer:
Thus, following the same divide by four relationship as in 60 : 15, the correct completion of the analogy 60 : 15 :: 100 : ? is 25.