Balancing of a chemical equation is based on which of the following laws?

Q. Assertion :The balancing of chemical equations is based on law of conservation of mass. Reason: Total mass of reactants is equal to total mass of products.

Q. Balancing of a chemical equation is based on which of the following law?

Q. A balanced chemical equation is in accordance with the law of conservation of mass.

Q. The chemical equations are balanced to satisfy one of the following laws in chemical reactions. This law is known as:
(a) law of conservation of momentum
(b) law of conservation of mass
(c) law of conservation of motion
(d) law of conservation of magnetism

Q. We know that balancing of a chemical equation is entirely based on law of conservation of mass. However, the concept of Principle of Atom Conservation (POAC) can also be related to law of conservation of mass in a chemical reaction. So, POAC can also act as a technique for balancing a chemical equation. For example, for a reaction: $AB{C}_3\to AB+C_2$.
On applying POAC for A, B & C and relating the 3 equations, we get : $\frac{n_{AB{C}_3}}{2}=\frac{n_{AB}}{2}=\frac{n_{C_2}}{3}$
$(n_x:$ number of moles of X). Thus, the coefficients of $AB{C}_3,AB\&C_2$ in the balanced chemical equation will be 2, 2 & 3 respectively and the balanced chemical equation can be represented as: $2AB{C}_3\to 2AB+3C_2$.
Now, answer the following question: Which of the following relation is correct regarding the numerical coefficients p,q,r in the balanced chemical equation: $pA+q{B}_2\to r{A}_2{B}_5$