Ratio and proportion(অনুপাত-সমানুপাত) in Mathematics for competitive examination/SSC CGL BankRail Food supply SI

Ratio:-
A relation between two quantities of similar type which shows that one quantity is how much times the other quantity,is known as ratio. Ratio is denoted by colon(:) .

Simplest form of ratio:-
If there is no common factor between the prior and post terms of a ratio, then the ratio is in its simplest form.

 Example.  24:22=12:11
If each term of ratio is multiplied or divided by a non zero number,then the ratio remains unaltered.

Types of ratio
1. Compound ratio
2. Duplicate ratio
3. Sub duplicate ratio
4. Triplicate ratio
5. Sub triplicate ratio
6. Inverse ratio or Reciprocal ratio
Proportion:-
Proportion is the equality of two ratios . As a:b =c:d , we write a:b::c:d and we say that a,b,c and d are in proportion. Here
a×d=b×c.

Short tricks:-

1. If A:B=a:b and B:C=m:n then A:B:C=am:mb:nb


2. If A:B=a:b and B:C=m:n and C:D=r:s then A:B:C:D= amr:bmr:bnr:bns

3. If X is distributed in the ratio a:b:c then 
First part =aX/(a+b+c)
Second part =bX/(a+b+c)
Third part =cX/(a+b+c)

Now some questions here for competitive exam

Q 1. If a quantity is devided in the ratio 3:5 ,the larger part is 75. Find the quantity.


Answer:-

Large quantity=5x
 small =3x
As per question,
5x=75
:. x=15
Quantity=3x+5x
                =8x
                 =8×15=120

Q 2. Marks of two candidates P and Q are in the ratio 2:5 . If the marks of P are 120, marks of Q are...... ?

Answer:-

Let the marks of P and Q be 2x and 5x.
According to question ,
 2x =120
or, ,x =60.

Therefore, marks of Q =5x =5×60= 300.


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