If, in a certain code language, ‘HERO’ is coded as 10800 then what is the code for ‘ZERO’?

1. Break Down the Problem

We need to understand how the word 'HERO' is transformed into the number 10800 and apply the same logic to the word 'ZERO'.

2. Relevant Concepts

To decode 'HERO' and find 'ZERO', we should analyze the individual letters. A common method in coding problems involves converting letters to their numerical positions in the alphabet (A=1, B=2, ..., Z=26).

3. Analyze and Detail

Step 1: Find the alphabetical positions of the letters in 'HERO':

• H = 8
• E = 5
• R = 18
• O = 15

Step 2: Multiply these positions together: $8 \times 5 \times 18 \times 15$

Step 3: Calculate the product:

• First, calculate $8 \times 5 = 40$
• Then, $40 \times 18 = 720$
• Finally, $720 \times 15 = 10800$

This confirms the coding method for ‘HERO’.

Step 4: Now, apply the same method to 'ZERO':

• Z = 26
• E = 5
• R = 18
• O = 15

Step 5: Multiply these positions together: $26 \times 5 \times 18 \times 15$

Step 6: Calculate the product:

• First, calculate $26 \times 5 = 130$
• Then, $130 \times 18 = 2340$
• Finally, $2340 \times 15 = 35100$

4. Verify and Summarize

The calculations yield the product for 'ZERO' as 35100.

Final Answer

The code for 'ZERO' is 35100.