A compound contains three elements $ A $ , $ B $ and $ C $ ,if the oxidation of $ A=+2,B=+5 $ and $ C=-2 $ , the possible formula of the compound is:
(A) $ {{A}_{3}}{{\left( {{B}_{4}}C \right)}_{2}} $
(B) $ {{A}_{3}}{{\left( B{{C}_{4}} \right)}_{2}} $
(C) $ {{A}_{2}}{{\left( B{{C}_{3}} \right)}_{2}} $
(D) $ AB{{C}_{2}} $

Hint: We will solve this question by calculating the oxidation state of all of these compounds. The oxidation state of the compound must be equal to the net charge of the compounds which is 0 in this case. We shall check the total charge of each of the options given.

Complete Step-by-Step solution
The following oxidation states are provided to us in the question
The oxidation state of element $ A=+2 $
The oxidation state of element $ B=+5 $
The oxidation state of element $ C=-2 $
According to the question, the net charge of each of these compounds is zero.
That is
The oxidation state of each of the compounds should also be equal to zero
Now, let us calculate the oxidation state of each of the given chemical compounds
The oxidation state for $ {{A}_{3}}{{\left( {{B}_{4}}C \right)}_{2}} $ can be calculated as:
 $ 3\times \left( +2 \right)+2\left[ 4\times \left( +5 \right)+\left( -2 \right) \right] $
Upon solving, the oxidation state of $ {{A}_{3}}{{\left( {{B}_{4}}C \right)}_{2}}=42 $
The result is not equal to $ 0 $
So, this is not the correct formula of the required chemical compound
The oxidation state for $ {{A}_{3}}{{\left( B{{C}_{4}} \right)}_{2}} $ can be calculated as:
 $ 3\times \left( +2 \right)+\left[ +5+4\times \left( -2 \right) \right]\times 2 $
Upon solving, the oxidation state of $ {{A}_{3}}{{\left( B{{C}_{4}} \right)}_{2}}=0 $
The result is equal to $ 0 $
This can be the correct formula of the required chemical compound
The oxidation state for $ {{A}_{2}}{{\left( B{{C}_{3}} \right)}_{2}} $ can be calculated as:
 $ 2\times \left( +2 \right)+2\times \left[ +5+3\times \left( -2 \right) \right] $
Upon solving, the oxidation state of $ {{A}_{2}}{{\left( B{{C}_{3}} \right)}_{2}}=+2 $
The result is not equal to $ 0 $
So, this is not the correct formula of the required chemical compound
The oxidation state for $ AB{{C}_{2}} $ can be calculated as:
 $ +3+5+2\times \left( -2 \right) $
Upon solving, the oxidation state of $ AB{{C}_{2}}=4 $
The result is not equal to $ 0 $
So, this is not the correct formula of the required chemical compound
Hence, the correct option is (B).

Note
In a chemical compound, the oxidation state or oxidation number of an atom provides insight into the number of electrons it has lost and, therefore, describes the extent of the atom's oxidation. If all of its bonds to other atoms are completely ionic in nature, the oxidation state of an atom can be defined as the hypothetical charge that would be held by that atom.