Seven years ago, Prachi was four times as old as her daughter was at that time. Four years from now, Prachi will be twoand-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
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 69.
Let, the present age of Prachi is P and her daughter's age is D
Prachi's age 7 years ago = P - 7
Daughter's age 7 years ago = D - 7
According to the condition,
⇒ P - 7 = 4(D - 7)
⇒ P - 7 = 4D - 28
⇒ P = 4D - 21.........(1)
Now,
Prachi's age 4 years from now = P + 4
Daughter's age 4 years from now = D + 4
According to the condition,
⇒ P + 4 = 5/2 × (D + 4)
⇒ 2(P + 4) = 5(D + 4)
⇒ 2P + 8 = 5D + 20
⇒ 2P = 5D + 12.......(2)
From eq 1
⇒ P = 4D - 21 (put in eq 2)
⇒ 2(4D - 21) = 5D +12
⇒ 8D - 42 = 5D + 12
⇒ 8D - 5D = 12 + 42
⇒ 3D = 54
⇒ D = 18
Put the value of D in eq 1
⇒ P = 72 - 21
⇒ P = 51
Now,
The sum of their present ages,
⇒ P + D = 51 + 18 = 59
Thus, the sum of their present ages is 69 years.