Question

Five years ago p was 5 times older than l. In ten years l will be 4/7 as old as p. What are the current ages of l and p?

Answer 1

Answer:
`(110)/(13),(290)/(13)`

Explanation:

Let
`a_(I)` be the present age of I.

Let
`a_(p)` be the present age of P.

`5` years ago P was
`5` times older than l.

Age of P
`5` years ago is
`a_(p)-5`

Age of I
`5` years ago is
`a_(I)-5`

`5* (a_(I)-5)=a_(p)-5\\5a_(I)=a_(p)+20` ....(i)

After
`10` years l will be
`(4)/(7)` as old as P.

Age of P
`10` years after is
`a_(p)+10`

Age of I
`10` years after is
`a_(I)+10`

`a_(I)+10=(4)/(7)* (a_(p)+10)\\ 7a_(I)+30=4a_(p)` ...(ii)

using (i) and (ii),

`7a_(I)+30=4(5a_(I)-20)\\110=13a_(I)\\a_(I)=(110)/(13)years`

`a_(P)=5a_(I)-20=5* (100)/(13)-20=(290)/(13) years`