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:$\dfrac{110}{13},\dfrac{290}{13}$

Step-by-step 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 $a_{I}-5$

$5\times (a_{I}-5)=a_{p}-5\\5a_{I}=a_{p}+20$     ....(i)

After $10$ years l will be $\frac{4}{7}$ as old as P.

Age of P $10$ years after is $a_{p}+10$

Age of I $10$ years after is $a_{I}+10$

$a_{I}+10=\frac{4}{7}\times (a_{p}+10)\\ 7a_{I}+30=4a_{p}$     ...(ii)

using (i) and (ii),

$7a_{I}+30=4(5a_{I}-20)\\110=13a_{I}\\a_{I}=\frac{110}{13}years$

$a_{P}=5a_{I}-20=5\times \frac{100}{13}-20=\frac{290}{13} years$