What is the difference between law of definite proportion, law of multiple proportion and law of reciprocal proportion?

The law of constant proportions states that when a compound is broken, the masses of the constituent elements remain in the same proportion. Or, in a chemical compound, the elements are always present in definite proportions by mass.

This means each compound has the same elements in the same proportions, regardless of where the compound was obtained, who prepared it, or its mass.

This law was formulated and proven by Joseph Louis Proust in 1799.

A person living in Australia sent a 100\text{ ml}100 ml sample of \ce{CaCO3}CaCOX3​(calcium carbonate) to a person living in India. The person living in India made his own sample of 200\text{ ml}200 ml and compared it to his friend's sample. Which of the two compounds has a greater ratio of \ce{Ca}:\ce{C}?Ca:C?

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Both contain equal ratios of \ce{Ca}Ca and \ce CC. This is guaranteed by the law of constant proportions.

The law of multiple proportions states that when two elements form two or more compounds between them, the ratio of the masses of the second element in each compound can be expressed in the form of small whole numbers.

This law was proposed by John Dalton, and it is a combination of the previous laws.

Carbon combines with oxygen to form two different compounds (under different circumstances). One is the most common gas \ce{CO2}COX2​ and the other is \ce{CO}CO. 

We know that the mass of carbon is 12\text{ u}12 u and the mass of oxygen is 16\text{ u}16 u. 
So, we can say that 12\text{ g}12 g of carbon combines with 32\text{ g}32 g of oxygen to form \ce{CO2}COX2​. 
Similarly, 12\text{ g}12 g of carbon combines with 16\text{ g}16 g of oxygen to form \ce{CO}CO.

So, the ratio of oxygen in the first and second compound is 2:1=\frac{32}{16}= 2,2:1=1632​=2, which is a whole number. 

The law of reciprocal proportions states that when two different elements combine with the same quantity of the third element, the ratio in which they will do so will be the same or a multiple of the proportion in which they combine with each other.

This law was proposed by Jeremias Ritcher in 1792.

Oxygen and sulfur react with copper to create copper oxide and copper sulfide, respectively. Sulfur and oxygen also react with each other to form \ce{SO2}.SOX2​. Therefore,

\begin{array}{rrcr} \text{in } \ce{CuS}, & \ce{Cu}:\ce{S} &=& 63.5:32 \\ \text{in } \ce{CuO}, & \ce{Cu}:\ce{O} &=& 63.5:16 \\\\ \Rightarrow &\ce{S}: \ce{O} &=& 32:16 \\ & &=&2:1. \end{array}in CuS,in CuO,⇒​Cu:SCu:OS:O​====​63.5:3263.5:1632:162:1.​

Now in \ce{SO2},SOX2​, we have

\ce{S}:\ce{O} = 32:32= 1:1.S:O=32:32=1:1.

Thus the ratio between the two ratios is the following:

\frac{2}{1} :\frac{1}{1} = 2:1,12​:11​=2:1,

which is a simple multiple ratio.