In a certain code language, 'DOCTOR' is coded as '101' and 'LEARN' is coded as '86'. How will 'STUDENT' be coded in that code language?

The correct answer is 119.

To determine how 'STUDENT' is coded, let us analyze the pattern used to code the words 'DOCTOR' and 'LEARN' based on the positional values of letters in the English alphabet (where A = 1, B = 2, C = 3, ..., Z = 26).

Step 1: Analyze the code for 'DOCTOR'
First, find the sum of the positional values of the letters in 'DOCTOR':
D = 4
O = 15
C = 3
T = 20
O = 15
R = 18

$\text{Sum of positional values}=4+15+3+20+15+18=75$

The coded value given for 'DOCTOR' is 101.
The difference between the coded value and the sum of letter positions is:

$101-75=26$

Step 2: Analyze the code for 'LEARN'
Next, find the sum of the positional values of the letters in 'LEARN':
L = 12
E = 5
A = 1
R = 18
N = 14

$\text{Sum of positional values}=12+5+1+18+14=50$

The coded value given for 'LEARN' is 86.
The difference between the coded value and the sum of letter positions is:

$86-50=36$

Step 3: Identify the relationship pattern
Observe the relationship between the number of consonants in each word and the value added to the sum of positional values:
- In 'LEARN', there are 3 consonants (L, R, N). The added value is 36.
- In 'DOCTOR', there are 4 consonants (D, C, T, R). The added value is 26.
Notice that for each additional consonant, the value added decreases by 10. The formula for the added value is:

$\text{Added Value}=66-(10\times \text{Number of Consonants})$

For 3 consonants: $66-(10\times 3)=36$
For 4 consonants: $66-(10\times 4)=26$

Step 4: Calculate the code for 'STUDENT'
Now, apply the exact same rule to 'STUDENT'.
Find the sum of positional values of the letters in 'STUDENT':
S = 19
T = 20
U = 21
D = 4
E = 5
N = 14
T = 20

$\text{Sum of positional values}=19+20+21+4+5+14+20=103$

Next, count the consonants in 'STUDENT':
The consonants are S, T, D, N, T (total of 5 consonants).
Using the established formula, calculate the added value for 5 consonants:

$\text{Added Value}=66-(10\times 5)=16$

Finally, add this value to the sum of positional values of 'STUDENT':

$\text{Code for STUDENT}=103+16=119$

Thus, 'STUDENT' is coded as 119.