Question

Joe's age , Joe's sister's age and Joe's father age sums upto a century. When son is as old as his father, Joe's sister will be twice as old as now, When Joe's is as old as his father then his father is twice as old as when his sister was as old as her father. Find age of each.

• A. 20, 30, 50
• B. 30, 20, 50
• C. 25, 25, 50
• D. 30, 15, 55
• E. Answer Required

Answer 1

The correct option is C 25, 25, 50

Let Joe's, Joe's sister and Joe's father age are x, y and z respectively.

So, we have

$x+y+z=100$ ............ (i)

When $x=z$ then $y=2y$

Substituting in equation (i) we get

$x+2y+z=100$ i.e.

$x+y=50$ .............. (ii)

Hence from (i) and (ii) we get

$z=50$

When $x=z$ then $x=2x$

From (i) we get

$2x+y+x=100$ i.e.

$3x+y=100$ .............. (iii)

Solving equations (ii) and (iii) we get

$x=25$

and then from (ii)

$y=25$.

Thus, 25, 25, 50 are the ages of each.

Hence, option 'C' is correct.