11 Plus Exams Forum

Ben's father was 33 when Ben was born. 8 years ago Ben's father was twice as old as Ben is now. How old is Ben?

Any answers greatly appreciated

SleepyHead

Say, Ben is B and Father is F.
Say, B = x, and then F = (x+33).

Eight years ago it was like this:
(X+33) - 8 = 2x
X +33 - 8 = 2x
X + 25 = 2x
25 = 2x-x
25 = x

So Ben is now 25, and his Father is now 25+ 33 = 58. Eight years ago Father was 50, which is 25 x 2.

(No doubt, Father got lots of grey hair after pushing his DS Ben through selective exams )

Excellent thanks, will explain to DD, who now thinks mummy can't do the 11+

Use logic rather than algebra - algebra is not necessary!

diagrams help a lot too

Guest55 wrote:Use logic rather than algebra - algebra is not necessary!

Can you explain how you would do this using logic rather than algebra? I think in algebra - although obviously less formally - as does DS1. But DD is different and I wouldn't really know how else to explain it well to her.

Thanks.

Hi

Well I said the difference in their ages is 33 - but we are looking at one of them 8 years ago.

33 - 8 = 25

So effectively a difference of 25 - so that's Ben's age and his Dad then was 50.

Thank you so much. That still took me ages to think through. I could see that you were right, but it still took me time to convince myself that there were no other options going that route. I think I have just proved the argument for why people need different methods to see which suits them best. If DD finds this sort of reasoning easier than algebra then I shall be back for some more help in a couple of years. It should be so obvious - maybe I am just tired? (Desperately trying to think of excuses for myself).

Age problems are always tricky - the algebra method would have been easier to follow if Ben's age = b so dad = b+ 33.

Using 'x' for the unknown just makes it harder! Always use letters that link with what they represent ..

Sorry, Guest55, I was using letters the way i did above as i was educated abroad and that was the way we were taught algebra - we were always using x for unknown. Hope no mistake there, just a matter of custom and convenience.