# Time and Work Important Formulas

Updated on Kisan Patel

In most of the problems on time and work, either of the following basic parameters are to be calculated :

If A can do a piece of work in X days, then A’s one day’s work = \(\frac{1}{X}\) ^{th} part of whole work.

If A’s one day’s work = \(\frac{1}{X}\) ^{th} part of whole work, then A can finish the work in X days.

If A can do a piece of work in Xdays and B can do it in Y days then A and B working together will do the same work in \(\frac{XY}{X+Y}\) days.

If A, B and C can do a work in X, Y and Z days respectively then all of them working together can finish the work in

\(\frac{XYZ}{XY+YZ+XZ}\)If (A + B) can do a piece of work in X days, (B + C) can do a place of work in Y days and (C + A) can do apiece of work in Z days. Then, (A + B + C) can do a piece of work in \(\frac{2XYZ}{XY+YZ+XZ}\) days.

If A and B together can do a piece of work in X days and A alone can do it in Y days, then B alone can do the work in \(\frac{XY}{Y-X}\) days.

If (A + B + C) can do a piece of work in X days and (B + C) can do a piece of work in Y days then A can do apiece of work \(\frac{XY}{Y-X}\) days.

A and B can do a work in ‘X’ and ‘Y’ days respectively. They started the work together but A left ‘a’ days before completion of the work. Then, time taken to finish the work is \(\frac{Y\left ( X + a \right )}{X + Y}\)

If ‘A’ is ‘a’ times efficient than B and A can finish a work in X days,then working together, they can finish the work in \(\frac{aX}{a + 1}\) days.

If A is ‘a’ times efficient than B and working together they finish a work in Z days then, time taken by \(A = \frac{Z\left ( a + 1 \right )}{a}\) days. and time taken by B = Z(a + 1) days.

If A working alone takes ‘x’ days more than A and B together, and B working along takes ‘y’ days more than A and B together then the number of days taken by A and B working together is given by \(\left [ \sqrt{xy} \right ]\) days.

**Quantitative Aptitude**