Explanation:

Explanation: 
Days of A : B = 40 : 100 = 2 : 5
Days in which A can complete work  = 2x, and B = 5x 
They complete the work in 2 days with their efficiencies doubling the second day.
So (1/2x + 1/5x) + (1/4x + 1/10x) = 1/2  
Solve, x = 21/10 days
So A does work in 2 * 21/10 days = 21/5 days and B in 5 * 21/10 = 21/2 days
So together:
5/21 + 2/21 = 7/21 = 1/3 work in 1 day or whole work in 3 days