Question

Who is oldest among three persons A, B, C now? Statements: (I) 10 years ago A is five years older to B. (II) 7 years from now B is 8 years younger to C.

• A. Statement (I) alone is sufficient to answer the question, but (II) alone is not sufficient.
• B. Statement (II) alone is sufficient to answer the question, but (I) alone is not sufficient.
• C. Both the statements (I) and (II) are sufficient to answer the question, but neither statement alone is sufficient.
• D. Both the statements (I) and (II) together are not sufficient to answer the question and additional data are required.

Hint:

When comparing ages, first convert all statements into present-age equations. This makes comparison easier.

Answer 1

The Correct Option is C

Concept: In age-related questions, the difference in ages between two persons always remains constant. To determine who is oldest, we must compare the present ages of A, B, and C.

Step 1: Checking Statement (I).
Given: \[ 10 \text{ years ago A was 5 years older than B} \] So, \[ (A-10)=(B-10)+5 \] \[ A=B+5 \] Thus, A is 5 years older than B. But there is no relation with C. So, Statement (I) alone is not sufficient.

Step 2: Checking Statement (II).
Given: \[ 7 \text{ years from now B will be 8 years younger than C} \] So, \[ (B+7)=(C+7)-8 \] \[ B=C-8 \] \[ C=B+8 \] Thus, C is 8 years older than B. But there is no relation with A. So, Statement (II) alone is not sufficient.

Step 3: Checking both statements together.
From Statement (I): \[ A=B+5 \] From Statement (II): \[ C=B+8 \] Comparing: \[ C=B+8 > A=B+5 \] Thus: \[ C>A>B \] So, C is oldest. Hence, both statements together are sufficient, but neither alone is sufficient.