Ratio and Proportion problems shortcuts

Here are some very important ratio and proportion problems shortcuts

If a number x is divided in the ratio a:b ,then

1^st part will be=ax/(a+b)

2^nd part will be= bx/(a+b)

Or if the number x is divided in three ratios as a:b:c , then

1^st part will be=ax/(a+b+c)

2^nd part will be=bx/(a+b+c)

3^rd part will be= cx/(a+b+c)

The ratio of milk to water in a mixture is A:B . if P liters of water is added to the mixture, then milk to water mixture ratio becomes A:C ,

then the quantity of milk in the mixture is

=AP/(C-B)           liters

And the quantity of water in the mixture is

= BP/(C-B)           liters