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Question – 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 ?

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 – 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 ?

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 – 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?

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.

( As Shobhna and Aswin are facing problem in solving this question, I am solving this question with second method which is also very easy, hope this will make the solution lot easier.)

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.

You can solve every time and work question with this trick. In above examples I wrote even simple calculations. While in exams you can do these calculations mentally and save lots of time.

Question – 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 ?

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 – 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?