TIME AND WORK

 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.