If the word FRIEND is coded as HUMJTK in a certain code language, then how is the word CANDLE written in that same code?

Introduction / Context:
This is a well known coding and decoding question often seen in competitive examinations. The word FRIEND is coded as HUMJTK, and you must find the code for CANDLE. The transformation is based on shifting each letter forward in the alphabet by an increasing number of positions, which is a standard pattern in such questions.

Given Data / Assumptions:
Original word: FRIEND.
Code word: HUMJTK.
Target word: CANDLE.
All letters are in uppercase, and the same rule must be applied to obtain the code for CANDLE.
Alphabet positions are taken as A = 1, B = 2, C = 3 and so on up to Z = 26.

Concept / Approach:
To discover the rule, compare each letter of FRIEND with the corresponding letter of HUMJTK and express the change in terms of alphabet positions. If a consistent pattern emerges, such as adding 2 to the first letter, adding 3 to the second letter and so on, then apply the same pattern to the letters of CANDLE. This approach uses basic arithmetic on alphabet indices.

Step-by-Step Solution:
Step 1: Write FRIEND and HUMJTK in two rows and compare letter by letter. Step 2: F becomes H. F is the 6th letter and H is the 8th letter, so the shift is +2 positions. Step 3: R becomes U. R is 18 and U is 21, so the shift is +3 positions. Step 4: I becomes M. I is 9 and M is 13, giving a shift of +4 positions. Step 5: E becomes J. E is 5 and J is 10, a shift of +5 positions. Step 6: N becomes T. N is 14 and T is 20, which is a shift of +6 positions. Step 7: D becomes K. D is 4 and K is 11, a shift of +7 positions. Step 8: Thus, the rule is: starting from the first letter of the word, shift forward by 2 positions, then 3, 4, 5, 6 and 7 positions respectively for the six letters. Step 9: Apply the same pattern to CANDLE. The letters are C, A, N, D, L and E. Step 10: C is 3. Shift it +2 positions: 3 + 2 = 5, which is E. Step 11: A is 1. Shift it +3 positions: 1 + 3 = 4, which is D. Step 12: N is 14. Shift it +4 positions: 14 + 4 = 18, which is R. Step 13: D is 4. Shift it +5 positions: 4 + 5 = 9, which is I. Step 14: L is 12. Shift it +6 positions: 12 + 6 = 18, which is R. Step 15: E is 5. Shift it +7 positions: 5 + 7 = 12, which is L. Step 16: Putting these letters together, the code for CANDLE is EDRIRL.

Verification / Alternative check:
To verify, you can quickly reapply the discovered pattern to FRIEND. Starting from F and adding 2 gives H, adding 3 to R gives U, and continuing with shifts of 4, 5, 6 and 7 produces M, J, T and K. This exactly reconstructs HUMJTK, confirming that the rule is correct. Therefore, the same rule applied to CANDLE must produce the correct code EDRIRL.

Why Other Options Are Wrong:
DCQHQK, ESJFME and DEQJQM: None of these strings can be obtained by applying the increasing forward shifts (+2, +3, +4, +5, +6, +7) to the letters of CANDLE. When you test them, the letter positions fail to match, so they do not follow the required pattern.

Common Pitfalls:
Students sometimes assume a fixed shift for all letters instead of noticing the increasing pattern. Others may miscount alphabet positions or forget to wrap around only when needed. Here, all shifts keep the letters inside the range A to Z without wrap around, which makes the pattern easier to verify. Careful counting and systematic checking for each letter prevent careless mistakes.

Final Answer:
Using the same pattern that converts FRIEND to HUMJTK, the word CANDLE is written as EDRIRL.