Seven years ago, Prachi was four times as old as her daughter was at that…
2024
Seven years ago, Prachi was four times as old as her daughter was at that time. Four years from now, Prachi will be two-and-a-half times as old as her daughter would then be. Find the sum of the present ages (in years) of Prachi and her daughter.
- A.
69
- B.
77
- C.
49
- D.
72
Attempted by 10 students.
Show answer & explanation
Correct answer: A
Define Variables:
Let P be Prachi's present age.
Let D be her daughter's present age.
Formulate Equations:
Seven years ago: Prachi was 4 times as old as her daughter.
Equation: P - 7 = 4 * (D - 7).
Four years from now: Prachi will be 2.5 times as old as her daughter.
Equation: P + 4 = 2.5 * (D + 4).
Solve the System:
Solving these equations yields D = 13 and P = 56.
The sum of their present ages is P + D = 56 + 13 = 69.