Question

A is five times as old as B. after 10 years a will be 3 times as old as B will be then. find their present age

Answer 1

$given \: that \: \\ a = 5b \\ after \: 10 \: years \\ a + 10 = 5b + 10 \\ also \: given \: that \: a \: is \: 3 \: times \: old \: as \: b \\ therefore \\ a + 10 =3(5b + 10) \\ 5b + 10 = 15b + 30 \\ 5b - 15b = 30 - 10 \\ - 10b = 20 \\ b = \frac{20}{ - 10} = - 2 \\ since \: age \: cant \: be \: in \: negative \\ b = 2 \: years \\ therefore \\ since \\ \: a = 5b \\ a = 5(2) \\ a = 10 \: years$

Answer 2

a=5b------------>1

after 10 years a will be 3 times as old as B

a+10=3(b+10)---------->2

on solving this equation we get b=10 and a=50