A-person-is-said-to-be-n-years-old-where-n-is-a-non-negative-integer-if-the-person-has-lived-at-least-n-years-and-has-not-lived-n-1-years-At-some-point-Tom-is-4-years-old-and-John-is-three-times-

Question Number 517 by Yugi last updated on 25/Jan/15

A p e r s o n i s s a i d t o b e n y e a r s o l d (w h e r e n i s a n o n - n e g a t i v e i n t e g e r) i f

t h e p e r s o n h a s l i v e d a t l e a s t n y e a r s a n d h a s n o t l i v e d n + 1 y e a r s . A t s o m e p o i n t

T o m i s 4 y e a r s o l d a n d J o h n i s t h r e e t i m e s a s o l d a s M a r y . A t a n o t h e r t i m e,

M a r y i s t w i c e a s o l d a s T o m a n d J o h n i s f i v e t i m e s a s o l d a s T o m . A t a t h i r d

t i m e, J o h n i s t w i c e a s o l d a s M a r y a n d T o m i s t y e a r s o l d . W h a t i s t h e l a r g e s t

p o s s i b l e v a l u e o f t ?

Commented by prakash jain last updated on 23/Jan/15

T, J, M a r e a g e s o f T o m, J o h n a n d M a r y

p_{1}

T_{1} = 4

J_{1} = 3 M_{1}

p_{2} L e t u s s a y k y e a r s f r o m p_{1}

T_{2} = 4 + k

M_{2} = 2 T_{2} = 8 + 2 k

J_{2} = 5 T_{2} = 20 + 5 k

M_{1} = 8 + 2 k - k = 8 + k

J_{1} = 20 + 5 k - k = 20 + 4 k

M_{1} = 8 + 2 k - k = 8 + k

J_{1} = 3 M_{1} \Rightarrow 20 + 4 k = 24 + 3 k \Rightarrow k = 4

M_{1} = 12, J_{1} = 36, M_{2} = 16, J_{2} = 40, T_{2} = 8

p_{3} L e t u s s a y l y e a r s f r o m p_{1}

T_{3} = t = 4 + l

J_{3} = 2 M_{3}

J_{3} = J_{1} + l = 36 + l

M_{3} = M_{1} + l = 12 + l

36 + l = 2 (12 + l)

36 + l = 24 + 2 l \Rightarrow l = 12

S o t = 4 + 12 = 16

Answered by prakash jain last updated on 23/Jan/15

S e e c o m m e n t o n l y o n e s o l u t i o n t = 16

Commented by prakash jain last updated on 23/Jan/15

T_{3} = t = 16

M_{3} = 24

J_{3} = 48