A mother is 25 years older than her daughter. Five years ago, the mother's age was six times the daughter's age. What is the mother's present age?
Verbal Reasoning
Problems on Ages
Difficulty: Medium
Choose an option
-
A25 years
-
B29 years
-
C32 years
-
D35 years
-
ENone of these
Answer
Correct Answer: 35 years
Explanation
Introduction / Context:We combine a difference-of-ages condition with a past multiple relation. Express both conditions as equations and solve for present ages.
Given Data / Assumptions:
- Mother is 25 years older than daughter now.
- Five years ago, mother's age was six times daughter's age.
Concept / Approach:Let present ages be M and D. Then M = D + 25, and M − 5 = 6(D − 5). Solve for D first, then compute M.
Step-by-Step Solution:
M = D + 25M − 5 = 6(D − 5)Substitute: (D + 25) − 5 = 6D − 30D + 20 = 6D − 30 ⇒ 50 = 5D ⇒ D = 10Therefore, M = 10 + 25 = 35Verification / Alternative check:
Five years ago: Mother 30, Daughter 5 ⇒ 30 = 6*5 ✓Why Other Options Are Wrong:
- 25, 29, 32 years do not satisfy the six-times relation with a 25-year difference.
- None of these: 35 fits perfectly.
Common Pitfalls:Using M − D = 25 but forgetting to subtract 5 from both in the past relation; or replacing “six times” with “six more.”
Final Answer:35 years