Ratio and proportions questions are asked in many exams including competitive exams like IBPS, SSC etc. and also other qualifying exams. These ratio and proportion 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 shortcut tricks to solve these ratio and problems problems if they are preparing for competitive exams like ssc or ibps etc. The ratio
and proportions problems 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.

Some of the AWESOME

SHORTCUT TRICKS ARE GIVEN HERE.
Shortcut Method of Solving number of Coins in a sum of money is discussed here
all the shortcut tips and tricks are discussed here

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.

Stay tuned for more to come soon.

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