Ratio and proportions questions are asked in many exams including competitive exams like IBPS, SSC etc. and also other qualifying exams. These problems takes a little more time to solve if the candidate does not know the shortcut trick to solve these problems.

It is very important for any candidate to learn the

These can be solved easily with the applications of the shortcut formulas provided below. Please remember them if you want to solve ratio and proportion questions faster and want to save time in your exams so that you can do more questions and ultimately attempt most questions in your exams,

then you need to learn Shortcut Tricks to solve questions quickly.

**shortcut tricks to solve ratio and problems problems**if they are preparing for competitive exams like from SSC and IBPS etc.These can be solved easily with the applications of the shortcut formulas provided below. Please remember them if you want to solve ratio and proportion questions faster and want to save time in your exams so that you can do more questions and ultimately attempt most questions in your exams,

then you need to learn Shortcut Tricks to solve questions quickly.

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.

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