If A can do a job in 10 day then in one day A can do 1/10th of job.

Question 1 - A take 5 days to complete a job and B takes 10 days to complete the same job. In how much time they will complete the job together?
Solution - A's efficiency = 20%, B's efficiency = 10%. If they work together they can do 30% of the job in a day. To complete the job they need 3.33 days.
Question 2 - A is twice as efficient as B and can complete a job 30 days before B. In how much they can complete the job together?
Solution - Let efficiency percentage as x
A's efficiency = 2x and B's efficiency = x
A is twice efficient and can complete the job 30 days before B. So,
A can complete the job in 30 days and B can complete the job in 60 days
A's efficiency = 1/30 = 3.33%
B's efficiency = 1/60 = 1.66%
Both can do 5% (3.33% + 1.66%) of the job in 1 day.
So the can complete the whole job in 20 days (100/5)
Question 3 - A tank can be filled in 20 minutes. There is a leakage which can empty it in 60 minutes. In how many minutes tank can be filled?
Solution - Method 1 Efficiency of filling pipe = 20 minutes = 1/3 hour = 300%
Efficiency of leakage = 60 minutes = 100%
We need to deduct efficiency of leakage so final efficiency is 200%. We are taking 100% = 1 Hour as base so answer is 30 minutes.
Method 2 Efficiency of filling pipe = 100/20 = 5% Efficiency of leakage pipe = 100/60 = 1.66% Net filling efficiency = 3.33% So, tank can be filled in = 100/3.33% = 30 minutes
You can change the base to minutes or even seconds.

Question 4 - 4 men and 6 women working together can complete the work within 10 days. 3 men and 7 women working together will complete the same work within 8 days. In how many days 10 women will complete this work?
Solution - Let number of men =x, number of women = y
Efficiency of 4 men and 6 women = 100/10 = 10%
So, 4x+6y = 10
Above equation means 4 men and 6 women can do 10% of a the job in one day.
Efficiency of 3 men and 7 women = 100/8 = 12.5%
So, 3x+7y = 12.5
By solving both equations we get, x = -0.5 and y = 2
Efficiency of 1 woman(y) = 2% per day
Efficiency of 10 women per day = 20%
So 10 women can complete the job in 100/20 = 5 days
Question 5 - A and B together can complete a task in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the same task in 30 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone?

Solution - Efficiency of A and B = 1/20 per day = 5% per day ___________1 Efficiency of B and C = 1/30 per day = 3.33% per day_________2 Efficiency of C and A = 1/30 per day = 3.33% per day_________3 Taking equation 2 and 3 together B + C = 3.33% and C + A = 3.33% C and 3.33% will be removed. Hence A = B Efficiency of A = B = 5%/2 = 2.5% = 1/40 Efficiency of C = 3.33% - 2.5% = 0.833% = 1/120 A can do the job in 40 days and C can do the job in 120 days he they work alone. Ratio of number of days in which A and C can complete the job 1:3.