Question 763091
Let Lakshmi's age be x years
Let her mother's age be y years.

Given: Mother is currently 3 times as old as Lakshmi.

So, {{{y = 3*x}}} ------ 1

Also given: 5 years ago, mother was 5 times as old as Lakshmi

So, {{{5*(x-5) = y-5}}}
    or 5*x - 25 = y-5
    or {{{5*x-y = 20}}} -------- 2

Substituting y = 3x in eqn. 2, we get:

5*x - 3*x = 20 or 2*x = 20

So, x = 10 years and y = 3*x = 30 years.

So, Lakshmi's present age = 10 years
Her mother's present age = 30 years.    

:)