Question

please answer fast..with explanation..
otherwise don't ​

Answer 1

Question-

• A and B can do a piece of work in 10hours, B and C can do it in 15 hours, while A and C can take 12hours to complete the work. B can complete the work in ?

Answer-

Given:

• (A+B) can complete a piece of work in 10 hours.
• (B+C) can complete a piece of work in 15 hours.
• (A+C) can complete a piece of work in 12 hours.

Therefore,

• (A+B)'s one hour work = 1/10 of total
• (B+C)'s one hour work = 1/15 of total
• (A+C)'s one hour work = 1/12 of total

To Find:

• How many hour will B take to complete work alone ?

Solution:

We are given that (A+B), (B+C) and (A+C) can complete a work in 10hours, 15hours and 12hours respectively and we found that (A+B), (B+C) and (A+C)'s one hour work is 1/10, 1/15 and 1/12 respectively.

Finding together one day's work :

(A+B)+(B+C)+ (A+C)'s one hour work = $\large{\sf{ \frac{1}{10} + \frac{1}{15} + \frac{1}{12}}}$

$\implies\small{\sf{2(A+B+C)'s~one~hour~work~=~\dfrac{6+4+5}{60}}}$

$\implies\small{\sf{2(A+B+C)'s~one~hour~work~=~\dfrac{15}{60}}}$

$\implies\small{\sf{2(A+B+C)'s~one~hour~work~=~\dfrac{1}{4}}}$

$\implies\small{\sf{(A+B+C)'s ~one~hour~work~=~\dfrac{1}{4×2}=\dfrac{1}{8}~part}}$

________________

Now, we found that (A+B+C)' one hour work is 1/8 where (A+C)'s one hour work is 1/12 .

Therefore,

$\small{\sf{(A+B+C)'s~one~hour~work~=~\dfrac{1}{8}}}$

[(A + C)'s one hour work is 1/12]

$\implies\small{\sf{\dfrac{1}{12}}+B~=~\dfrac{1}{8}}$

$\implies\small{\sf{B's~one~hour~work~=~\dfrac{1}{8}-\dfrac{1}{12}}}$

$\implies\small{\sf{B's~one~hour~work~=~\dfrac{3-2}{24}}}$

$\implies\small{\sf{B's~one~hour~work~=~\dfrac{1}{24}}}$

Hence,

• $\small{\boxed{\tt{\green{B~will~take~24~hours~to~complete~work~alone}}}}$