Question

A can do a complete a work in 20 days. B can complete the work in 30 days.A and B can complete together in hiw many days?​

Answer 1

$\large \sf \underline{Question}$

A can do a complete a work in 20 days. B can complete the work in 30 days . A and B can complete together in how many days ?

$\rule{200pts}{2pts}$

Answer

$= \colorbox{red}{ \rm 12 \: days}$

☯︎ Solution

Let's understand the question through Unitary Method in terms of 1 day work , it is given that :

A takes 30 days to complete a unit work - 1 work.

➪ This implies that,

• In 1 day A can do 1/30 th of the work.

Similarly,

B takes 20 days to complete a unit work - 1 work.

➪ This implies that,

• In 1 day B can do 1/20th of the work

According to 1 day work ,

A and B can together do 1/20 + 1/30 = 5/60 th of the work .

$\footnotesize\dfrac{1}{20} + \dfrac{1}{30} = \dfrac{1 \times 3 + 1 \times 2}{60} = \dfrac{5}{60}$

So if 5/60 th of a work can be done by both A & B in 1 day .

This means that, to do 1 work they would take

$: \implies \footnotesize \rm \dfrac {5}{60}th \: of \: work = 1 \: day \\ \footnotesize \rm1 \: work = \cancel\dfrac{60}{5} = \red{12 \: days}$

☯︎ Conclusion

Therefore, A and B , together can do the same unit work in 12 days .

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Thankyou