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

If a number x is added to a ratio a:b so that the ratio becomes c:d ,

Then   x= (ad-bc)/(c-d)

If there are two numbers whose sum and difference is a and b respectively,

 then the ratio of those numbers will be = (a+b)/(a-b)

if two quantities A and B are in the ratio a:b ,

then

(A+B):(A-B)::(a+b):(a-b)

If two numbers are given in the ratio a:b and P in both numbers, the ratio becomes c:d ,

Then

1^st number = aP(c-d)/(ad-bc)

2^nd number = bP(c-d)/(ad-bc)

Sum of numbers = [P(a+b)(c-d)]/(ad-bc)

Difference of numbers = [P(a-b)(c-d)]/(ad-bc)

If the ratio of incomes of two persons is a:b , and also ratio of their expenses is c:d , and each person saves a sum of x rupees,

Then

Income of 1^st person  = ax(d-c)/(ad-bc)

Income of 2^nd person = bx(d-c)/(ad-bc)

Example:

In a mixture of milk and water, ratio of milk to water is 5:1 . if 5 liters of water is added to the mixture, the ratio becomes 5:2. Determine the quantity of milk in mixture initially?

Solution:

So in the given question, A=5, B=1, C=2, P=5

Now putting the formula as given above

Quantity of milk = AP/(C-B) = (5*5)/(2-1) = 25 liters

So the answer is

25 liters of milk is there in the initial mixture of milk and water.