Question

If in a certain code language, \[ \text{DELHI}=45 \] \[ \text{MUMBAI}=63 \] then the code for \[ \text{PATNA} \] is:

• A. \(45\)
• B. \(55\)
• C. \(60\)
• D. \(66\)

Hint:

In coding-decoding questions, always test multiple patterns before selecting one. The simplest valid pattern is often the correct one.

Answer 1

The Correct Option is A

Concept: Coding-Decoding questions test pattern recognition and logical analysis. The hidden pattern may involve letter positions, number values, counting vowels, alphabetical sums, or a combination of these ideas.

Step 1: Write alphabetical positions. For DELHI: \[ D=4,\;E=5,\;L=12,\;H=8,\;I=9 \] Sum: \[ 4+5+12+8+9 = 38 \] The code is: \[ 45 \] Difference: \[ 45-38=7 \]

Step 2: Check MUMBAI. \[ M=13,\; U=21,\; M=13,\; B=2,\; A=1,\; I=9 \] Sum: \[ 13+21+13+2+1+9 = 59 \] Code: \[ 63 \] Difference: \[ 63-59=4 \] The pattern is not consistent.

Step 3: Search for another relationship. Observe: DELHI has: \[ 5 \text{ letters} \] \[ 5\times9=45 \] MUMBAI has: \[ 7 \text{ letters} \] \[ 7\times9=63 \] Hence: \[ \text{Code} = (\text{Number of letters}) \times9 \]

Step 4: Apply to PATNA. PATNA contains: \[ 5 \] letters. Therefore: \[ 5\times9 = 45 \] However, 45 is not present among the options. Hence there is again an inconsistency in the options.

Step 5: Final conclusion. Using the identified pattern: \[ \boxed{45} \] would be the correct code.