Question

A can do a work in 6 days and B can do in 8 days . they worked together for 2 days and then B left the job. how many days would A require to finish the work​

Answer 1

Answer :

In 2¹/₂ days, A alone can finish the remaining work.

Step-by-step explanation :

Given,

• A can do a work in 6 days
• B can do work in 8 days
• They worked together for 2 days and then B left the job

To find,

• how many days would A require to finish the work ?

Solution,

➟ A can do a work in 6 days

The amount of work A can do in one day = 1/6

➟ B can do a work in 8 days

The amount of work B can do in one day = 1/8

➟ Together, the amount of work can be done in one day

          $= \dfrac{1}{6}+\dfrac{1}{8} \\\\\\ =\dfrac{8+6}{48} \\\\\\ =\dfrac{14}{48} \\\\\\ =\dfrac{2 \times 7}{2 \times 24} \\\\\\ =\dfrac{7}{24}$

Therefore; in one day, the amount of work done A and B can do = 7/24

➟ In 2 days,

           $= 2 \times \dfrac{7}{24} \\\\\\ =\dfrac{7}{12}$

the amount of work A and B can do in 2 days = 7/12

The remaining work = 1 - 7/12

          = (12 - 7)/12

          = 5/12

It is given, A can do work in 6 days

   In how many days A can do 5/12 work ?

       = 6 × (5/12)

       = 5/2

       = 2.5 days

∴ A alone can finish the remaining work in  $2 \dfrac{1}{2}$   days.