Linked present and future ages with a given fraction: The present age of X is 2/3 of Y's present age. After 6 years, X will be 46 years old. Find Y's current age.

Introduction / Context:This age problem uses a present fractional relationship and a future absolute age for one person. Determine X now from the future value, then use the fraction to compute Y now.

Given Data / Assumptions:

• X now = (2/3) × Y now.
• X after 6 years = 46 ⇒ X now = 40.

Concept / Approach:Back-calculate X's present age, then invert the fraction to find Y: Y = (3/2) × X.

Step-by-Step Solution:1) X now = 46 − 6 = 40.2) 40 = (2/3) × Y ⇒ Y = 40 × (3/2) = 60.3) Therefore, Y's present age is 60 years.

Verification / Alternative check:After 6 years: X = 46, Y = 66; the original fraction at present is 40/60 = 2/3 (correct).

Why Other Options Are Wrong:

• 40/56/100/48 do not satisfy the fraction 2/3 when X is 40 now.

Common Pitfalls:Confusing “X is 2/3 of Y” with “Y is 2/3 of X” or forgetting to move back 6 years before applying the fraction.

Final Answer:60 years