Important Facts And Formulae :-
1. If A can do a piece of work in N days.
Then, Work done by A in 1 day = $\frac{1}{N}$
2. If A can do a piece of work in M days and B can do it in N days.
Then, A and B working together will do the same work in $\frac{MN}{M+N}$ days.
For Eg. A can do a piece of work in 12 hours and B alone can do it in 15 hours. In how much time will they finish the whole work, working together?
Sol. A's 1 hour's work = $\frac{1}{12}$
B's 1 hour's work = $\frac{1}{15}$
(A + B)'s 1 hour's work = $\frac{1}{12}+\frac{1}{15}$
= $\frac{5+4}{60}$
= $\frac{9}{60}$
= $\frac{3}{20}$
$\therefore $ Working together, they will finish the work in $\frac{20}{3}$hours
i.e. 6 hours 40 min.
3. If A, B and C can do a work in M, N and P days respectively, Then, all of them working together can finish the work in $\frac{MNP}{(MN+NP+MP)}$ days.
For Eg. If A can do a piece of work in 5 days, B can di it in 6 days and C can do the same work in 12 days. How long will they take to complete the work?
Sol. According to formulae
= $\frac{5\times6\times12}{5\times6+6\times12+5\times12}$
= $\frac{360}{162}$
= $2\frac{2}{9}$days
4. Let A be twice as good a workman as B. Then,
- Ratio of work done by A and B in the same time = 2:1
- Ratio of time taken by A and B to do a piece of work = 1:2
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