The ratio of the present ages of a mother and daughter is 7 : 1. Four years ago, the ratio of their ages was 19 : 1. What will be the mother’s age four years from now?

Introduction: Two time-separated ratios allow us to set up equations for present ages. With linear relationships, solve for the scale factor and compute the asked future age.

Given Data / Assumptions:

• Present: M : D = 7 : 1 → M = 7k, D = k.
• Four years ago: (M − 4) : (D − 4) = 19 : 1.
• We seek M + 4.

Concept / Approach: Substitute M and D into the past ratio and solve for k. Then compute the mother’s current age and add 4 years.

Step-by-Step Solution:

Verification / Alternative check: Four years ago: Mother 38, Daughter 2 → ratio 38 : 2 = 19 : 1, correct.

Why Other Options Are Wrong: 42, 38, 36, 48 correspond to present or past ages or incorrect scaling; asked value is mother’s age 4 years hence.

Common Pitfalls: Using 4 years instead of subtracting 4 in the “four years ago” ratio or mixing present/future ages.

Final Answer: 46 years