Pooja's age 4 years back and Deepa's age after 4 years are equal. The ratio of Pooja's age 4 years hence and Deepa's age 4 years before is 3 : 1. What is the ratio of their present ages?

let the present age of Pooja and Deepa are x and y respectively

4 years ago age of pooja = x - 4

4 years ago age of Deepa = y - 4

4 years hence Pooja's age = x + 4

4 years hence Deepa's age = y + 4

Pooja's age 4 years back and Deepa's age after 4 years are equal == x - 4 = y + 4

solving, x - y = 8...............(1)

ratio of Pooja's age 4 years hence and Deepa's age 4 years before is 3 : 1

$$ \frac{ x + 4}{y - 4} = \frac{3}{1} $$

solving, 3y - x = 16...............(2)

from (1) and (2) 

x = 8 + y

16 = 3y - (8 + y)

16 = 3y - 8 - y

24 = 2y

y = 12

x = 20

ratio of their present ages = 20 : 12

                                       = 5 : 3