A project will take Mr A and Mr B 12 days to complete. Now that both of them work for 4 days, with the rest to be completed by Mr A in 10 days, find the number of days Mr B take to complete this project by himself.

Answer: 5 days

Step-by-step explanation:

If a project will take Mr A and Mr B 12 days to complete, this means that

1/A + 1/B = 1/12

(A+B) / AB = 1/12

AB / (A+B) = 12

Cross multiply

AB = 12A + 12B ... (1)

Now that both of them work for 4 days. Part of the job completed is

AB / (A+B) = 4

AB = 4A + 4B ... (2)

Minus equation 2 from 1

8A + 8B = 0 ... (3)

The remaining day = 8 days

If Mr A can complete this in 10 days,

The number of days Mr B take to complete this project will be

1/10 + 1/B = 1/8

1/B = 1/8 - 1/10

1/B = (10 + 8) / 80

B = 80/18

B = 4.444 days

Approximately 5 days