1 yr ago, the ratio between mother and daughter age was 4 : 1. The ratio of their ages after 4 yr will be 3 : 1. Find the ratio of their ages 5 yr ago?

Let the present age of mother be x and daughter be y.
From question,
(x - 1)/(y - 1) = 4/1
⇒ x - 1 = 4(y - 1)
⇒ x = 4y - 3 ......(i)
Again from question,
(x + 4)/(y + 4) = 3/1
∴ x + 4 = 3(y + 4)
⇒ x = 3y + 8 ..(ii)
On Solving Eqs. (i) and (ii), we get y = 11 and x = 41
∴ Ratio of their ages 5 yr ago = (x - 5)/(y - 5) = 36/6 = 6/1 = 6 : 1