Time and Work Shortcut with examples

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Time and Work

A can do a piece of work in 5 days, and B can do it in 6 days. How long will they take if both work together?

 

A’s 1 day’s work  = \frac { 1 }{ 5 }

th part of whole work and

B’s 1 day’s work \frac { 1 }{ 6 } th part of whole work

(A+B)’s one day’s work =\frac { 1 }{ 5 } +\frac { 1 }{ 6 } =\frac { 11 }{ 30 } th part of whole work. so, both together will finish the work in

\frac { 30 }{ 11 } days=2\frac { 8 }{ 11 }

By Direct Formula

A+B can do the  work in \frac { 5x6 }{ 5+6 } days=\frac { 30 }{ 11 } =2\frac { 8 }{ 11 }

Two men, Vikas and Vishal, working separately can mow a field in 8 and 12 hours respectively. If they work in stretches of one hour alternately, Vikas beginning at 8 a.m, when will the mowing be finished?

 

In the first hour, Vikas mows\frac { 1 }{ 8 }  of the field.

In the second hour, Vishal mows \frac { 1 }{ 12 } of the field

in the first two 2 hours \frac { 1 }{ 8 } +\frac { 1 }{ 12 } =\frac { 5 }{ 24 } of the field is mown

In 8 hours \frac { 5 }{ 24 } x4=\frac { 5 }{ 6 } of the field is mown

 

Now, \left[ 1-\frac { 5 }{ 6 }  \right] =\frac { 1 }{ 6 } of the field remains to be mown

in the 9th hour, vikar mows \frac { 1 }{ 8 } of the field

Remaining work = \frac { 1 }{ 6 } -\frac { 1 }{ 8 } =\frac { 1 }{ 24 }

Vishal will finish the remaining work in \left( { \frac { 1 }{ 24 }  }/{ \frac { 1 }{ 12 }  } \right)

or  \frac { 1 }{ 2 } of an hour

The total time required is \left[ 8+1\frac { 1 }{ 2 }  \right] or\quad 9\frac { 1 }{ 2 }

Thus the work will be finished at \left[ 8+1\frac { 1 }{ 2 }  \right] or\quad 17\frac { 1 }{ 2 } \quad or\quad 5.30\quad pm

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