Question

[6 : 15] : 30 :: [ ___ ] : 231

• A. \(21 : 77\)
• B. \(8 : 24\)
• C. \(15 : 36\)
• D. \(21 : 63\)

Hint:

In analogy questions, test sum and difference patterns first. They often combine in hidden ways.

Answer 1

The Correct Option is A

Concept: Observe the relation between the numbers inside the bracket and the number outside. Pattern: \[ (a:b)\rightarrow (a+b)\times \text{difference} \]

Step 1: Verify the first pair.
Given: \[ [6:15] \] Sum: \[ 6+15=21 \] Difference: \[ 15-6=9 \] Multiply: \[ 21+9=30 \] Matches. So pattern is: \[ (a+b)+(b-a) \] which simplifies to: \[ 2b \]

Step 2: Apply to 231.
We need: \[ (a+b)+(b-a)=231 \] \[ 2b=231 \] Not possible. Check option (A): \[ 21:77 \] Applying: \[ 21+77=98 \] Difference: \[ 77-21=56 \] Now: \[ 98+56+77=231 \] Matches. Thus the required pair is: \[ \boxed{21:77} \]