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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
Question

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

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 = 271.5\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

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