## Time and Distance Shortcuts

###
**METHOD 1**

**M1 persons do a work in D1 days**and

**M2 persons do the same work in D2 days**then

we have the equation

**M1*d1= M2* D2**

###
**METHOD 2**

**M1 persons**can do

**W1 work in D1 days**and

**M2 persons**can do

**W2 work in D2 days**then

we have (

**M1 D1)/W1 = (M2 D2)/W2**###
**METHOD 3**

if

**A**can do a work in**x days**,**B**can do a work in**y days**then**A and B together**(A+B) can do the same work in

**( xy )/(x+y)**days

###
**METHOD 4**

**A alone**can do a work in

**x days**,

**A+B**can do a work in

**y days**then .

**B alone**can do the work in

**(xy)/(x-y)**

###
**METHOD 5**

**here A+B means A and B working together**

if A working alone takes

**x days more than (A+B)**and B working alone takes**y days more than (A+B)**then
the number of days taken by A and B together is given by

**root of**(xy)

###
**METHOD 6**

**here A+B+C means A B C working together**

**A**can do a work in

**x days**,

**B**can do the same work in

**y days**,

**C**can also do the same work in

**z days**then

A+B+C can do the work in

**(xyz)/(****xy+yz+zx)****days**###
**METHOD 7**

**here A+B+C means A B C working together**

A+B can do a work in

**x days**, B+C can do the work in**y days**, C+A can do the work in**z days**then**A+B+C**can do the work in

**(2xyz )/**

**xy+yz+zx**days

###
**METHOD 8**

if

**x1 men or y1 women**can reap the field in D days ,then**x2 men and y2 women**take to reap it in

**D(x1y1)/(**

**x2 y1+x1 y2)**days

###
**M****ETHOD 9**

a certain men can do a work in

**D days**if there are**x me**n**less**it could be finished in d days more,then
the no of men orginaly are

**x(D+d)/d**###
**METHOD 10**

a certain men can do a work in

**D days**if there are**x men****more**it could be finished in d days more,then
the no of men orginaly are

**x(D-d)/d**###
**METHOD 11**

if

**x1 men**or**x2 women**or**x3 boys**can do a work in**D days**then
1 men + 1 women + 1 boy can do the same work in

**d(x1x2x3)/(****x1x2+x2x3+x3x1)**
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