Step-by-step Solution:

Quick Solution

This age puzzle can be solved by translating the given information into a system of two algebraic equations.

1. Set Up the Equations

- Let the mother's present age be M and the daughter's present age be D.

• From the first sentence, "The sum of ages ... is 63 yr":
  M + D = 63 --- (Equation 1)
• From the second sentence, "Four years back, the mother's age was 4 times that of daughter's age":
  The mother's age was (M - 4) and the daughter's was (D - 4).
  M - 4 = 4(D - 4) --- (Equation 2)

2. Solve the Equations

- First, let's simplify Equation 2:
M - 4 = 4D - 16
M = 4D - 12

- Now, substitute this expression for M into Equation 1:
(4D - 12) + D = 63
5D - 12 = 63
5D = 75
D = 15 (The daughter's age is 15).

- Finally, use the daughter's age to find the mother's age with Equation 1:
M + 15 = 63
M = 63 - 15 = 48.

3. Verification (Optional)

- Present ages: Mother=48, Daughter=15. Sum = 63. This is correct.
- Four years ago: Mother=44, Daughter=11. Is 44 = 4 × 11? Yes. The answer is correct.

Final Answer: The present age of the mother is 48 yr.