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Question

A can do a piece of work in 14 days which B can do in 21 days. They begin together and work at it for 7 days. Then, A fell ill and B had to complete the work. In how many days, the work was completed? 


Solution

A can do in $$14$$ days
In $$1$$ day A can do $$\cfrac { 1 }{ 14 } th$$ work
B an do in $$21$$ days
In $$1$$ day B can do $$\cfrac { 1 }{ 21 } th$$ work
In $$7$$ days they both do $$\cfrac { 7 }{ 14 } +\cfrac { 7 }{ 21 } th$$ of work
$$\cfrac { 5 }{ 6 } th$$ of work
B can do $$1$$ work in $$21$$ says
$$\cfrac { 1 }{ 6 } th$$ work in  $$\cfrac { 21 }{ 6 } $$ days
$$=\cfrac { 7 }{ 2 } =3.5$$ days
Total no. of days $$=7+3.5=10.5$$days

Mathematics

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