In a certain code language, ‘CAT’ is written as ‘24’ and ‘FROG’ is written as ‘50’. How will ‘TIGER’ be written in that code language?

The correct answer is 67.

To solve this coding-decoding problem, we first determine the alphabetical positional values (where A = 1, B = 2, C = 3, ..., Z = 26) of each letter in the given words and analyze the logic used to obtain the coded number.

Step 1: Analyze the code for ‘CAT’
Find the positional values of the letters in ‘CAT’:
C = 3
A = 1
T = 20
Sum of positional values = 3 + 1 + 20 = 24.
For a 3-letter word, the added extra value is 0.
Total code = 24 + 0 = 24.

Step 2: Analyze the code for ‘FROG’
Find the positional values of the letters in ‘FROG’:
F = 6
R = 18
O = 15
G = 7
Sum of positional values = 6 + 18 + 15 + 7 = 46.
For a 4-letter word, an additional value of 4 is added to the sum.
Total code = 46 + 4 = 50.

Step 3: Identify the underlying pattern
The coding pattern takes the sum of the alphabetical positions of all letters in the word and adds an extra value depending on the word length:
- 3-letter word (‘CAT’): Added value = 0
- 4-letter word (‘FROG’): Added value = 4
- 5-letter word (‘TIGER’): Added value = 8 (following an arithmetic progression increasing by 4 for each additional letter).

Step 4: Calculate the code for ‘TIGER’
Find the positional values of the letters in ‘TIGER’:
T = 20
I = 9
G = 7
E = 5
R = 18
Sum of positional values for ‘TIGER’:

$\text{Sum}=20+9+7+5+18=59$

Since ‘TIGER’ contains 5 letters, we add 8 to the sum of positional values:

$\text{Code for TIGER}=59+8=67$

Thus, ‘TIGER’ is written as 67 in that code language.