In a code language, 'BASIC' is coded as 101 and 'MAGIC' is coded as 102. How will 'LIGHT' be coded in the same language?
Correct Answer :
79
Solution :
The correct answer is Option 2: 79.
Let's understand the coding pattern by looking at the given words and their numerical codes.
First, we find the positional values of the letters of the English alphabet in standard order (where A = 1, B = 2, ..., Z = 26):
A = 1, B = 2, C = 3, D = 4, E = 5, F = 6, G = 7, H = 8, I = 9, J = 10, K = 11, L = 12, M = 13, N = 14, O = 15, P = 16, Q = 17, R = 18, S = 19, T = 20, U = 21, V = 22, W = 23, X = 24, Y = 25, Z = 26.
Now, let's analyze the word 'BASIC':
The alphabetical positions of its letters are:
B = 2
A = 1
S = 19
I = 9
C = 3
Let's find the sum of these positions:
Sum = 2 + 1 + 19 + 9 + 3 = 34.
To relate 34 to the given code of 101, let's consider the reverse positional values (where A = 26, B = 25, ..., Z = 1). The reverse positional value of a letter is calculated as (27 - standard position value):
B = 27 - 2 = 25
A = 27 - 1 = 26
S = 27 - 19 = 8
I = 27 - 9 = 18
C = 27 - 3 = 24
Let's find the sum of these reverse positions:
Sum of reverse positions = 25 + 26 + 8 + 18 + 24 = 101.
This matches the given code for 'BASIC' exactly!
Let's verify this logic with the word 'MAGIC':
The reverse positional values of its letters are:
M = 27 - 13 = 14
A = 27 - 1 = 26
G = 27 - 7 = 20
I = 27 - 9 = 18
C = 27 - 3 = 24
Sum of reverse positions = 14 + 26 + 20 + 18 + 24 = 102.
This also matches the given code for 'MAGIC' perfectly.
Now, we apply the same logic to code the word 'LIGHT':
Let's find the reverse positional values for each letter in 'LIGHT':
L = 27 - 12 = 15
I = 27 - 9 = 18
G = 27 - 7 = 20
H = 27 - 8 = 19
T = 27 - 20 = 7
Let's sum these values:
Sum = 15 + 18 + 20 + 19 + 7 = 79.
Therefore, 'LIGHT' will be coded as 79.
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