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. 

Correct option is A

Given:

​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.

Solution:

Let the current age of the daughter be x and Prachi be y.

So, as per the question,

Seven years ago,

Age of Prachi = y - 7

Age of her daughter = x - 7

Condition given, y - 7 = 4(x - 7)

y = 4x - 28 + 7 = 4x - 21

Now, four years from now,

Age of Prachi = y + 4

Age of her daughter = x + 4

Condition given, y + 4 = 2.5(x + 4)

y = 2.5x + 10 - 4 = 2.5x + 6 

Equating both the equations, we get

4x - 21 = 2.5x + 6

4x - 2.5x = 6 + 21

1.5x = 27

x = $$\frac{27}{1.5}$$​ = 18

So, y = 4 $$\times$$​ 18 - 21 = 72 - 2​ = 181 = 51

Sum of the ages of Prachi and her daughter = 51 + 18 = 69 years