Arvind is now 40 years old and Asha is 25 years old. How many years ago from now was Arvind four times as old as Asha?

10 years

20 years

15 years

25 years

APEDIA

NTPC Graduate Tier 1

2025 • 05 Jun, 2025 • Shift-3

Arvind is now 40 years old and Asha is 25 years old. How many years ago from now was Arvind four times as old as Asha?

Correct Answer

20 years

[Variable Initialization]: Let us define the unknown timeline as 'x' years ago. We must logically project their current ages backward into this historical timel......

💡 Analysis & Explanation

[Variable Initialization] ▼

Let us define the unknown timeline as 'x' years ago. We must logically project their current ages backward into this historical timeline.

[Age Backward Projection] ▼

Exactly 'x' years ago, Arvind's biological age would have been represented as (40 - x). Simultaneously, Asha's age would have been (25 - x).

[Constraint Formulation] ▼

The problem explicitly dictates that during that specific past year, Arvind was exactly four times Asha's age. This creates the linear algebraic equation: 40 - x = 4 × (25 - x).

[Equation Resolution] ▼

Expanding the right side yields 40 - x = 100 - 4x. Grouping the 'x' terms on the left and constants on the right: 4x - x = 100 - 40. This simplifies neatly to 3x = 60.

[Final Value Deduction] ▼

Dividing by 3, we discover x = 20.

Conclusion ▼

This mathematical condition occurred exactly 20 years ago.

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Arvind is now 40 years old and Asha is 25 years old. How many years ago from now was Arvind four times as old as Asha?