Mother told her daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be". Find the present ages of the mother and the daughter, respectively.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 42: 12
Let the present age of the mother and the daughter be M and D, respectively.
Given that
Seven years ago, Mother was seven times as old as her daughter
Three years from now, Mother shall be three times as old as her daughter
According to the question
⇒ M - 7 = 7 (D - 7)
⇒ M - 7 = 7D - 49
⇒ 7D - M = 49 - 7 = 42
⇒ 7D - M = 42 .......(1
Now, M + 3 = 3 (D + 3)
⇒ M + 3 = 3D + 9
⇒ M - 3D = 6 .......(2
Equation 1 + Equation 2
⇒ 4D = 48
⇒ D = 12
From Equation 2
⇒ M - 36 = 6
⇒ M = 42
Hence, the required ratio = 42 : 12