Question

X says to Y, “I am 3 times as old as you were 3 years ago”. How old is X?
I. Y’s age 17 years from now will be same as X’s present age.
II. X’s age nine years from now is 3 times Y’s present age.

• A. If the question can be answered with the help of statement I alone.
• B. If the question can be answered with the help of statement II alone.
• C. If both the statement I and statement II are needed to answer the question.
• D. If the question cannot be answered even with the help of both the statements.

Hint:

Translate the statements into algebraic equations and solve systematically. Often both are needed to uniquely determine the values.

Answer 1

The Correct Option is C

Let present age of X be $x$ years and Y be $y$ years.
From the main statement: \[ x = 3(y - 3) \quad \text{(1)} \Rightarrow x = 3y - 9 \] Now use Statement I: Y’s age 17 years from now = X’s present age \[ y + 17 = x \quad \text{(2)} \] Substitute equation (1) into (2): \[ y + 17 = 3y - 9
\Rightarrow 17 + 9 = 3y - y
\Rightarrow 26 = 2y \Rightarrow y = 13 \Rightarrow x = 3y - 9 = 30 \] Now verify Statement II: X’s age 9 years from now = 30 + 9 = 39
Y’s present age = 13
$3 \times y = 3 \times 13 = 39$ ✓ True Hence, both statements together help us find the unique values.