A mother's present age is three times her daughter's present age. Ten years from now, the mother's age will be exactly double her daughter's age. How old is the daughter today?

Introduction / Context:
This problem uses two simple relationships between the present ages of a mother and her daughter and their ages after 10 years. Such questions are typical in aptitude tests and are solved using linear equations in one variable, representing the daughter's age or the mother's age.

Given Data / Assumptions:

• The mother's present age is three times her daughter's present age.
• After 10 years, the mother's age will be twice her daughter's age at that time.
• We need to find the daughter's present age.

Concept / Approach:
Let the daughter's present age be D years. Then the mother's present age is 3D. After 10 years, the daughter will be D + 10 and the mother will be 3D + 10. The second condition says 3D + 10 = 2(D + 10). Solving this equation quickly yields D. This is a straightforward linear equation problem.

Step-by-Step Solution:
Let daughter's present age be D years. Then mother's present age is 3D years. After 10 years, daughter's age = D + 10 and mother's age = 3D + 10. Given that 10 years from now the mother's age is twice the daughter's age: 3D + 10 = 2(D + 10). Expand the right side: 3D + 10 = 2D + 20. Rearrange: 3D - 2D = 20 - 10. So D = 10. Therefore, the daughter's present age is 10 years.

Verification / Alternative check:
If the daughter is 10 years old now, the mother is 3 * 10 = 30 years old. After 10 years, the daughter will be 20 and the mother will be 40. Indeed, 40 is exactly twice 20, matching the second condition. Both statements in the problem are satisfied, confirming that 10 years is correct.

Why Other Options Are Wrong:
If the daughter were 8, the mother would be 24 and in 10 years their ages would be 18 and 34, which does not give a 2 : 1 ratio. Similar checks show that daughters of age 9, 11 or 12 lead to future ages that do not satisfy the doubling condition. Only D = 10 meets both the three times and the double conditions simultaneously.

Common Pitfalls:
Students sometimes reverse the relation and assume daughter's age is three times the mother's, which is impossible here. Another common mistake is to forget to add 10 to both ages or to misplace terms when simplifying the equation. Writing each step clearly and interpreting the words carefully avoids these errors.

Final Answer:
So, the daughter is 10 years old today.