In a certain coding scheme, the six letter word AMOUNT is written as BNPTMS. Using the same pattern of letter shifts applied to the first and second halves of the word, how is the word AROUND written in that code?

Introduction / Context:
This coding question uses a mixed shifting rule: the first half of the letters in the word are shifted forward in the alphabet while the second half are shifted backward. The word AMOUNT becomes BNPTMS under this rule. We must detect exactly how the shifts work and apply the same idea to the six letter word AROUND.

Given Data / Assumptions:

• AMOUNT is written as BNPTMS in the code.
• The word has six letters, naturally split into two halves of three letters each.
• The same coding rule must be applied to AROUND, which also has six letters.
• The mapping uses alphabet positions from A = 1 to Z = 26, with wrap around.
• We assume a consistent rule across corresponding positions.

Concept / Approach:
We compare AMOUNT with BNPTMS letter by letter. By computing the positional differences, we see how the first three letters are transformed and how the last three letters are transformed. This reveals a pattern of shifting forward for the first half and backward for the second half. Then we apply the same forward and backward shifts to the letters of AROUND.

Step-by-Step Solution:
Step 1: Split AMOUNT into two halves: AMO and UNT.Step 2: For the first half AMO, write positions: A = 1, M = 13, O = 15. For the corresponding coded letters BNP, the positions are B = 2, N = 14, P = 16.Step 3: The shift from A to B is +1, from M to N is +1 and from O to P is +1. So the first half letters are shifted forward by one position.Step 4: For the second half UNT, write positions: U = 21, N = 14, T = 20. For the coded letters TMS, positions are T = 20, M = 13, S = 19.Step 5: The shift from U to T is −1, from N to M is −1 and from T to S is −1. So the second half letters are shifted backward by one position.Step 6: Therefore, the coding rule is: for a six letter word, shift the first three letters forward by one and the last three letters backward by one.Step 7: Now apply this rule to AROUND. Split AROUND into ARO and UND.Step 8: For the first half ARO: A = 1, R = 18, O = 15. Shifting forward by one gives B = 2, S = 19 and P = 16, forming BSP.Step 9: For the second half UND: U = 21, N = 14, D = 4. Shifting backward by one gives T = 20, M = 13 and C = 3, forming TMC.Step 10: Combine the two halves BSP and TMC to form the coded word BSPTMC.

Verification / Alternative check:
A quick reverse check by shifting the letters of BSPTMC back in the opposite direction restores AROUND. B back to A, S back to R, P back to O, T forward to U, M forward to N and C forward to D. This confirms that the coding rule has been applied correctly and that BSPTMC is the valid code.

Why Other Options Are Wrong:
The options BSPUNT, BSUPTN, ZSPVOE and BSPUMT do not respect the exact pattern of +1 for the first three letters and −1 for the last three letters. Some shift all letters in the same direction while others alter only a few letters correctly. Because the coding scheme is fully systematic, any deviation in even one position makes the option invalid.

Common Pitfalls:
Some students try to shift all letters forward or all letters backward and therefore generate a partly correct but overall incorrect code. Others forget to treat the word as two separate halves. It is crucial to compare each position carefully and notice that the direction of shift changes halfway through the word.

Final Answer:
Using the same mixed shifting pattern as in AMOUNT, the correct code for AROUND is BSPTMC.