Question

A man does a piece of work in three days.

in one day, this man does ___of the work.
another man does the same work in 4 days.
in one day this man does _____of the work.
in one day both meant together do _____of the work.
both work together do the whole work in _____ days.​
explain it with step by step solution.

Answer 1

`\textsf{First man's work in one day: }\boxed{\sf (1)/(3)} \textsf{ of the work}`

`\textsf{Second man's work in one day: }\boxed{\sf (1)/(4)}\textsf{ of the work}`

`\textsf{Both men's work together in one day:}\boxed{\sf (7)/(12)}\textsf{ of the work}`

`\textsf{Both men together complete the work in }\boxed{\sf (12)/(7)}\textsf{ days,}`

Explanation:

First Man:

`\textsf{Time taken: 3 days}`

`\sf \textsf{Work done in one day:} (1)/(3)\textsf{ of W}`

(since he completes the work in 3 days)

`\dotfill`

Second Man:

`\sf \textsf{Time taken: 4 days}`

`\sf \textsf{Work done in one day:}( 1)/(4 )\textsf{of W }`

(since he completes the work in 4 days)

`\dotfill`

Both Men Together:

Work done in one day when working together: Work done by the first man + Work done by the second man

`\textsf{Work done in one day when working together: }\sf (1)/(3)\textsf{ of W }+ (1)/(4 )\textsf{ of W }`

`\sf\textsf{ Work done in one day when working together: } \sf (7)/(12 )\textsf{ of W }`

`\dotfill`

Time taken when Both Work Together:

`\texttt{Time taken by both: }\frac{\texttt{Total work }}{ \textsf{Work done in one day together.}}`

`\sf \textsf{Time taken by both: } =(1)/((7)/(12))`

`\sf \textsf{Time taken by both: } = (12)/(7) \textsf{ of W}`

`\dotfill`

Summary:

`\textsf{First man's work in one day: }\boxed{\sf (1)/(3)} \textsf{ of the work}`

`\textsf{Second man's work in one day: }\boxed{\sf (1)/(4)}\textsf{ of the work}`

`\textsf{Both men's work together in one day:}\boxed{\sf (7)/(12)}\textsf{ of the work}`

`\textsf{Both men together complete the work in }\boxed{\sf (12)/(7)}\textsf{ days,}`