Question

A can complete a work in 6 days .B
can complete the same work in 8 days
How many days will be required to
Complete the work , If they work together.
​

Answer 1

Question:

A can complete a work in 6 days , B can complete the same work in 8 days. How many days will be required to complete the work , if they work together.

Answer:

24/7 days

Solution;

It is given that A can complete a work in 6 days.

Thus;

=> Time taken by A to complete a work

= 6 days

=> One day work of A = (1/6) work

Also;

It is given that B can complete a work in 8 days.

Thus;

=> Time taken by B to complete a work

= 8 days

=> One day work of B = (1/8) work

Now,

One day work of A and B together

= (1/6) work + (1/8) work

= (1/6 + 1/8) work

= { (4 + 3)/24 } work

= (7/24) work

Thus;

The time taken by A and B together

= 24/7 days.

Hence,

A and B will together complete the work in 24/7 days.

Answer 2

$\bold{\underline{\underline{Answer:}}}$

Days required to complete the work is $\bold{\dfrac{24}{7}}$ or 3.42 (approx) days.

$\bold{\underline{\underline{Step\:by\:step\:explanation:}}}$

Given :

• A can complete a work in 6 days .
• B can complete the same work in 8 days

To find :

• Days required to complete the work if person A and person B work together.

Solution :

Person A takes 6 days to complete a piece of work.

•°• Work done by person A in one day,

$\rightarrow$$\bold{\dfrac{1}{6}}$ ---> (1)

Person B takes 8 days to complete a piece of work.

•°• Work done by person B in one day,

$\rightarrow$$\bold{\dfrac{1}{8}}$ ---> (2)

If they work together, the time taken to complain the work will be sum of person A's one day work and person B's one day work.

Adding equation (1) and (2)

$\rightarrow$$\bold{\dfrac{1}{6}}$ + $\bold{\dfrac{1}{8}}$

$\rightarrow$ $\bold{\dfrac{8+6}{8\times\:6}}$

$\rightarrow$ $\bold{\dfrac{14}{48}}$

$\rightarrow$ $\bold{\dfrac{7}{24}}$

•°• $\bold{\dfrac{24}{7}}$ days will be required for person A and person B to complete the work if they work together.

If we convert it further into decimals then our answer :-

$\rightarrow$$\bold{3.42}$ (approx) days.