Explanation:

Let the work done by Alekh, Alia and Aman in 1 day be x. y and z respectively  (Alekh’s 4 days + Alia’s 5 days + Aman’s 4 days) work = 1 
(Alekh + Alia) 4 days + (Alia + Aman) 1 day + Aman 3 days work = 1….. (1) 

From question:  Work done by Alekh and Alia in 1 day = 1/5  Work done by Alia and Aman in 1 day = 1/15 

In equation (1)  1/5 × 4 + 1/15 × 1 + 3z = 1 

4/5 + 1/15 + 3z = 1 

12/15 + 1/15 + 3z = 1 

13/15 + 3z = 1 

3z = 1-13/15  3z = 2/15 

z = 2/45 

Aman can do work in 5 days 

y + z = 1/15 

y + 2/45 = 1/15 

y = 1/15 – 2/45 

y = 3/45 – 2/45 

y = 1/45 

Days taken be Alia = 45 days