Different grades of concrete has different Concrete Mix proportions which means different concrete mix ratios. As Per IS456:2000,  the Concrete mix design has the following concrete mix proportions :-

Type of Concrete	Concrete Grade	Mix Ratio	Characteristic Compressive strength of Concrete @28Days in N/mm2
Ordinary concrete	M5	1:5:10	5 N/mm2
M7.5	1:4:8	7.5 N/mm2
M10	1:3:6	10 N/mm2
M15	1:2:4	15 N/mm2
M20	1:1.5:3	20 N/mm2
Standard Concrete	M25	1:1:2	25 N/mm2
M30	Design Mix	30 N/mm2
M35	Design Mix	35 N/mm2
M40	Design Mix	40 N/mm2
M45	Design Mix	45 N/mm2
M50	Design Mix	50 N/mm2
High Strength Concrete	M55	Design Mix	55 N/mm2
M60	Design Mix	60 N/mm2
M65	Design Mix	65 N/mm2
M70	Design Mix	70 N/mm2

Different types of  Concrete mixes:

Concrete Mixes are primarily divided into the two different types :

Nominal Mix: 

Nominal Mix is generally adopted for small scale constructions. In this type of mix, the mix ratios and concrete constituent proportions are prefixed and specified. Eg: M20(1:1.5:3);  the quantity of cement, sand and aggregate is batched in volume as per the fixed ratio 1:1.5:3. From the above table till M25 grade, the concrete proportions are called as Nominal mix concrete.

Design Mix: 

Design mix concrete is adopted for high rise constructions. In this type of mix, the mix ratios are decided by an Engineer after analysing the properties of individual ingredients of concrete. Like, cement is tested for Fineness modulus and Specific gravity of cement in the lab while deciding the Design mix ratio. There is No Pre-fixed ratio, and ingredients are are batched in weight. From the above table, concrete grades more than M25 falls in Design mix.
In Simple, Design Mix refers to the ratios which are decided by the designer.

Calculation of Quantities of Cement, Sand and Aggregate in 1m³ of concrete:-

To calculate the individual quantities of cement, sand and aggregate required for 1m³  assume a nominal mix grade of concrete such as M20. You can use same method to calculate any grade of concrete.   

Concrete Mix Design for M20 Grade Concrete:-

Now let us consider M20 grade concrete;

As per IS456:2000, M20 Grade concrete proportion is  = 1 : 1.5 : 3 

We have to add all the volume to know the total volume = 1 + 1.5 + 3 = 5.5

As we know that  during concreting when we place wet concrete, it gets harden after certain standard time. Considering the same it had be decided upon by Civil design Engineers to take a factor of safety ranging from 1.54 to 1.57 to counter that shrinkage.

i.e volume of dry Concrete = 1.54 to 1.57 times Volume of wet concrete

I am Assuming 1.57 as factor of safety

So total volume of concrete required is 1.57 m³

Calculation of Volume of Cement in 1m³ of Concrete:-

To calculate the Quantity of Cement in Concrete the following formula is used.

Volume of Cement

=   ^Cement⁄_{Cement+Sand+Aggregate}    x 1.57

For 1m³ of Concrete = 403.2Kgs of Cement is required.         

No. of Cement Bags required for 1m³ of Concrete  = 403/50 = 8.06 ~ 8 bags   

Hence we require 8 bags of cement for 1m³ of concrete.