Question

Judy is five times as old as Henry. In two years, she'll be three times as old, and in six years she'll only be twice as old. How old will Judy be in seven years?

Answer 1

Given:

Judy is five times as old as Henry.

Let age of Henry = $x$

So, age of Judy, $y$ = $5x$ ....... (1)

In two years, she'll be three times as old.

Age of Henry after 2 years = $x+2$

So, age of Judy, $y+2$ = 3($x+2$) ..... (2)

and in six years she'll only be twice as old.

$y+6=2(x+6)$ ..... (3)

To find:

Judy's age in seven years?

Solving (1) and (2):

$5x+2=3x+6\\\Rightarrow 2x=4\\\Rightarrow x = 2$

So, $y = 5x = 10$

In six years, age of Henry = 2 + 6 = 8 years

In six years, age of Judy = 10 + 6 = 16 years

Age of Judy in seven years = $y+7$ = 10 + 7 = 17 years