Time and Work

PIPES & CISTERNS:

Inlet Pipe: A pipe which is used to fill the tank is known as Inlet Pipe.

Outlet Pipe: A pipe which can empty the tank is known as an Outlet Pipe.

• If a pipe can fill a tank in 'x' hours then the part filled per hour= 1/x
• If a pipe can empty a tank in 'y' hours, then the part emptied per hour= 1/y
• If pipe A can fill a tank 'x' hours and pipe can empty a tank in 'y' hours, if they are both active at the same time, then

                                The part filled per hour  =$$\dfrac{1}{x}-\dfrac{1}{y}$$(if y>x)

                                The part emptied per hour  =$$\dfrac{1}{y}-\dfrac{1}{x}$$(if x>y)

• If X can do a work in 'n' days, the fraction of work X does in a day is $$\frac{1}{n}$$
• If X can do a work in 'x' days, and Y can do a work in 'y' days, the number of days taken by both of them together is $$\frac{x*y}{x+y}$$
• If $$A_1$$ men can do $$B_1$$ work in $$C_1$$ days and $$A_2$$ men can do $$B_2$$ work in $$C_2$$ days, then $$\frac{A_1 C_1}{B_1}$$ =$$\frac{A_2 C_2}{B_2}$$

Work:

• If X can do a work in 'n' days, the fraction of work X does in a day us 1/n

• If X can do a work in 'x' days, and Y can do a work in 'Y' days,

                       The number of days taken by both of them together is $$\frac{x*y}{x+y}$$

• If $$M_{1}$$ men work for $$H_{1}$$ hours per day and worked for $$D_{1}$$ days and completed $$W_{1}$$ work, and if $$M_{2}$$ men work for $$H_{2}$$ hours per day and worked for $$D_{2}$$ days and completed $$W_{1}$$ work, then

                                                      $$\frac{M_{1}H_{1}D_{1}}{W_{1}}$$=$$\frac{M_{2}H_{2}D_{2}}{W_{2}}$$