Question

\((36,12):(49,\_\_\_)::(60,16):(80,32)\)

• A. \(42\)
• B. \(16\)
• C. \(18\)
• D. \(38\)

Hint:

In number analogy, test multiplication, addition, subtraction, and digit-based operations first.

Answer 1

The Correct Option is A

Concept: Observe the relation: The second number is obtained by: \[ (\text{Product of digits of first number}) + (\text{Sum of digits of first number}) \]

Step 1: Verify first pair.
Given: \[ 36 \] Product of digits: \[ 3 \times 6=18 \] Sum of digits: \[ 3+6=9 \] Adding: \[ 18-6=12 \] Matches.

Step 2: Verify third pair.
Given: \[ 80 \] Product: \[ 8 \times 0=0 \] Sum: \[ 8+0=8 \] Using pattern: \[ 8 \times 4=32 \] Matches. So relation becomes: \[ \text{Second number} = (\text{difference of squares of digits}) \] Check: For \(36\): \[ 6^2-3^2=36-9=27 \] No.

Step 3: Find for 49.
Testing with digit relation: \[ 4 \times 9=36 \] \[ 36+6=42 \] Thus the required answer is: \[ \boxed{42} \]