Father says to his son: "When I will be as old as my dad is now, you will be 5 times older than right now, and your age will be 8 years older than I am right now. My father and mine ages sum is 100 years." Find son's age.

Question

zyberg · Answer

My attempt to solve this: 
D - grandfather's age; 
d - father's age; 
s - son's age. 

Then, I tried to make a system of equations: 
D = 5s, 
(D - d) + s = d + 8, 
D + d = 100. 

However, the solution for son that I find from this is 12. Then grandfathers age would be 12 * 5 = 60, however with that fathers age would need to be 40 and that doesn't make any sense with the second equation... Please help me to spot my mistakes!

jiteshmeghwal9 · Answer

Let father's age be x & that of son's be y & that of grandfather's age be z. Also let the difference between grandfather's age & father 's age be 't'.

x+y=100
z-x=t
Now when father will achieve the grandfather's age the son will be y+t years old or we can say that his age will be y+8 i.e; 8 years older than father's age
y+t=x+8
y+t=5y

zyberg · Answer

@jiteshmeghwal9 Solved your system of equations. x + y = 100 should be x + z = 100 tho. Another thing to notice that we get grandfather's age to be less than fathers... x = 78; z = 22

jiteshmeghwal9 · Answer

yeah tht was a typo

x+z=100
z-x=t

when father will achieve the grandfather's age , t years would have been passed from present time

x+8=y+t
y+t=5y

zyberg · Answer

@jiteshmeghwal9 as I said, I get that grandfather is thrice as old as the father, using your equations.

jiteshmeghwal9 · Answer

https://www.wolframalpha.com/input/?i=x%2Bz%3D100,z-x%3Dt,x%2B8%3Dy%2Bt,y%2Bt%3D5y

jiteshmeghwal9 · Answer

but yeah i was putting my opinion here 

I m not trying to confuse u

zyberg · Answer

Oh, thank you! Seems that I had made a mistake while solving them.

@ganeshie8, I think that the solution is right. Logically, it seems to make sense?

ganeshie8 · Answer

Yeah, jitesh's solution looks good to me.

I was hoping to get an integer answer... question appears to be wrong.

zyberg · Answer

Well, perhaps they tried to trick people into thinking that it is wrong to get non integer solutions... although I was hoping for that as well, but...