If NAMO is coded as 172 and OM is coded as 56, then using the same rule what should be the code for SHIVAY?

Introduction / Context:
This is a letter to number coding question, a standard part of many aptitude and reasoning tests. Each word is converted into a number using a fixed hidden rule, and you must infer that rule from the examples. Once the pattern is identified, you apply it to a new word to obtain its code. These questions train you to recognise numeric patterns associated with letter positions in the alphabet.

Given Data / Assumptions:
We are told that NAMO is coded as 172 and OM is coded as 56. The letters in these words are N, A, M, O and O, M respectively. We must deduce the coding rule that turns these letters into the numbers 172 and 56. After discovering the pattern, we must apply the same rule to the word SHIVAY to find its code. The options provided are 606, 415, 504, 404 and 312.

Concept / Approach:
A common approach in such problems is to replace each letter by its alphabetical position and then look for sums, products or combinations of these values. For example, A is 1, B is 2, C is 3 and so on up to Z as 26. Since both sample words give numbers that are larger than any single letter position, the rule likely involves adding the positions and then multiplying by the number of letters. We will test this idea on the given examples.

Step-by-Step Solution:
Write the positions for NAMO: N = 14, A = 1, M = 13 and O = 15. Compute their sum: 14 + 1 + 13 + 15 = 43. The given code for NAMO is 172. Notice that 43 multiplied by the number of letters (4) is 43 * 4 = 172, which matches perfectly. Now check OM: O = 15 and M = 13. Their sum is 15 + 13 = 28. There are 2 letters in OM. So 28 * 2 = 56, which matches the given code for OM. This confirms the rule: code(word) = (sum of letter positions) * (number of letters). Now apply it to SHIVAY. For SHIVAY, positions are S = 19, H = 8, I = 9, V = 22, A = 1 and Y = 25. The sum is 19 + 8 + 9 + 22 + 1 + 25 = 84. The word SHIVAY has 6 letters, so 84 * 6 = 504.

Verification / Alternative check:
As a verification step, re add the positions of SHIVAY carefully: 19 + 8 = 27, 27 + 9 = 36, 36 + 22 = 58, 58 + 1 = 59 and 59 + 25 = 84. Multiplying 84 by 6 again gives 504, confirming the previous computation. You can also briefly test whether any other simple rule could fit the examples, such as multiplying only by the first letter position or by a constant. None of those alternate patterns will successfully match both NAMO and OM. Therefore, the sum multiplied by word length rule is the only consistent and logical coding scheme here.

Why Other Options Are Wrong:
Codes 606, 415, 404 and 312 do not equal 84 multiplied by 6 and thus cannot arise from the discovered rule. For instance, 606 divided by 6 is 101, which is not the sum of any possible combination of letter positions in SHIVAY. Similarly, 404 divided by 6 does not yield an integer, showing it is incompatible with the pattern of sum times length. Since the pattern has been clearly established and verified on the sample words, any number not equal to 504 must be rejected. Thus only 504 is consistent with the coding logic.

Common Pitfalls:
A common mistake is to try overly complex operations such as squaring positions or mixing place values based on letter order, which leads to unnecessary confusion. Another pitfall is to test a pattern on only one example and assume it is correct without confirming it on the second example. Some students also miscalculate alphabet positions, especially beyond the middle of the alphabet, leading to incorrect sums. To avoid these issues, always verify your discovered rule against all given examples and recalculate alphabet positions slowly if needed. This disciplined approach greatly improves accuracy in coding and decoding questions.

Final Answer:
Using the same coding rule as in NAMO and OM, the code for SHIVAY is 504.