Ten years ago, a mother was four times as old as her daughter. Ten years from now, the mother will be twice as old as the daughter. What is the daughter's present age?

Introduction / Context:
Age problems with “times as old” at two different times usually form a pair of linear equations in present ages. Solving gives the required current ages.

Given Data / Assumptions:

• 10 years ago: Mother = 4 × Daughter
• In 10 years: Mother = 2 × Daughter

Concept / Approach:
Let present ages be M (mother) and D (daughter). Translate each time-based relation to an equation and solve simultaneously.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 5, 10, 30 do not satisfy both time-based multiplicative conditions.
• None of these: 20 works.

Common Pitfalls:
Using 4 times and 2 times on present ages instead of the specified past/future ages; or making arithmetic slips when substituting between equations.

Final Answer:
20 years