Question

a and b and c can do a piece of work in 6 days 12 days and 15 days respectively how long will it take to finish it if they work together​

Answer 1

Given:

• A can do a piece of work in 6 days.
• B can do a piece of work in 12 days.
• C can do a piece of work in 15 days.

To finD:

• how long they will take to finish the work if they will work together.

Solution:-

Given that A can do a piece of work in 6 days, B can do a piece of work in 12 days and C can do a piece of work in 15 days.

Now,

∵ A take 6 days to complete a work.

∴ A will complete $\large{\tt{\dfrac{1}{6}th}}$ part of work in 1 day.

_________

∵B take 12 days to complete a work

∴ B will complete $\large{\tt{\dfrac{1}{12}th}}$ part of work in 2 day.

_________

∵ C take 15days to complete a work

∴ C will complete $\large{\tt{\dfrac{1}{15}th}}$ part of work in 1 day.

_________

Now,

A,B and C will do part of work in 1 day =

$\large{\bf{\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{15}}}$

→ $\large{\bf{\dfrac{10+5+4}{60}}}$

→ $\large{\bf{\dfrac{19}{60}}}$

Therefore,

A,B and C will do $\large{\sf{\dfrac{19}{60}}}$ part of work in 1 day.

_________

Total time they will take to do whole work = 1÷part of work they did in 1 day.

=> Total time they will take to do work = $\large{\bf{1÷\dfrac{19}{60}}}$

=> $\large{\bf{1×\dfrac{60}{19}}}$

Therefore,

If A,B and C will work together, they will take $\large{\tt{\green{\dfrac{60}{19}}}}$ days to complete the work.