Question

A and B working separately do a piece of work in 9 and 12 days respectively. If they work for a day alternately, how many days will the work be completed with A beginning the work?

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Answer 1

Answer:A can complete work in 9 days.

So, percentage of work A compltes in one day = 100/9 = 11.11%.

B can complete work in 12 days.

B's one day work = 100/12 = 8.33%.

A and B together can complete = 11.11 +8.33 = 19.44% of work in one day.

Now,

Take 2 days = 1 unit of time (one day of A and one of B).

In one unit of time A and B can complete work = 19.44% work.

Total time unit they need to complete whole work = 100/(19.44) = 5 time unit aprox.

Thus, Total time = 5 time unit = 5 *2 = 10 days.

Step-by-step explanation:Fraction Method:

 

A can complete total work in 9 days.

One day work of A = 1/9 part.

B can complete work in 12 days.

One day work of B = 1/12 part.

A and B together can complete work in one day,

= 1/9 + 1/12

= (4 +3)/36 = 7/36 part.

Take, 2 days = 1 time unit.

To time unit needed to complete the work,

= 1/(7/36) = 36/7 = 5 time unit approx.

Total Time = 2 *5 = 10 days.

Answer 2

Answer:

A can complete work in 9 days.

So, percentage of work A compltes in one day = 100/9 = 11.11%.  

B can complete work in 12 days.  

B's one day work = 100/12 = 8.33%.  

A and B together can complete = 11.11 +8.33 = 19.44% of work in one day.  

Now,  

Take 2 days = 1 unit of time (one day of A and one of B).  

In one unit of time A and B can complete work = 19.44% work.  

Total time unit they need to complete whole work = 100/(19.44) = 5 time unit aprox.  

Thus, Total time = 5 time unit = 5 *2 = 10 days.  

Step-by-step explanation:Fraction Method:      

A can complete total work in 9 days.

One day work of A = 1/9 part.  

B can complete work in 12 days.

One day work of B = 1/12 part.

A and B together can complete work in one day,

= 1/9 + 1/12

= (4 +3)/36 = 7/36 part.

Take, 2 days = 1 time unit.

To time unit needed to complete the work,

= 1/(7/36) = 36/7 = 5 time unit approx.

Total Time = 2 *5 = 10 days.

Step-by-step explanation:

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