Question

a can do a piece of work in 10 days, B in 12 days and C in 15 days how long will it take them it together to complete it.​

Answer 1

that would depend on how long the project is

Answer 2

Question -:

A can do a piece of work in 10 days, B in 12 days and C in 15 days. How long will it take them it together to complete it ?

Explanation -:

We observe here that A can do the work in 10 days; B can do the same work in 12 days whereas C can do the same work in 15 days. We are asked to calculate how much time will it take if three of them will work together.

We will solve this problem with traditional method.

Let us solve the question.

`\small\pmb{ A's \: 1 \: day's \: work = (1)/(10)}`

`\small\pmb{ B's \: 1 \: day's \: work = (1)/(12)}`

`\small\pmb{ C's \: 1 \: day's \: work = (1)/(15)}`

`\small\sf{ (A + B + C)'s \: 1 \: day's \: work = \frak {(1)/(10)+(1)/(12) + (1)/(15)}}`

• L.C.M of 10, 12 and 15 is 60

`\longrightarrow \small\frak{ (6 + 5 + 4)/(60) }`

`\longrightarrow \small\frak{ (15)/(60) = (1)/(4) }`

• Hence A,B and C can finish the work in 4 days.

`\rule{40mm}{3pt}`

`\huge \star \: \large \underline{ \boxed{\bf{ Additional \: Information }}} \: \huge\star`

`\small \bf{\frak{ General \: Rules \: for \: Time \: and \: Work : }}`

• If a person can complete a work in x days, then in 1 day the person does 1/x of the work.
• If a person can complete 1/x of the work in 1 day, then the person requires x days to complete the work.
• If some persons work together to do a piece of work, then the money paid to them is divided among them in ratio of their one day's work

`\overline{ \underline{ \rule{72mm}{4pt}}}`