In a certain code language, ‘FARM’ is coded as HDTP and ‘EGGS’ is coded as GJIV. How will ‘FOOD’ be coded in the same language?

The correct option is HRQG.

To find the code for the word "FOOD", let us first analyze the pattern used in the given coding language by looking at the alphabetical positions of the letters.

Example 1: "FARM" is coded as "HDTP"

F (6th letter) + 2 = H (8th letter)
A (1st letter) + 3 = D (4th letter)
R (18th letter) + 2 = T (20th letter)
M (13th letter) + 3 = P (16th letter)

The pattern here is an alternating shift of +2 and +3 positions.

Example 2: "EGGS" is coded as "GJIV"

E (5th letter) + 2 = G (7th letter)
G (7th letter) + 3 = J (10th letter)
G (7th letter) + 2 = I (9th letter)
S (19th letter) + 3 = V (22nd letter)

This confirms the alternating pattern of +2, +3, +2, +3.

Now, let us apply this same pattern to the word "FOOD":

$F\left(6\right)+2=H\left(8\right)$

$O\left(15\right)+2=Q\left(17\right)$

Putting the letters together, "FOOD" is coded as HRQG.