To solve this problem, we need to understand the concept of neutralization reactions and the heat evolved during these reactions.

When an acid and a base react, they undergo a neutralization reaction to produce water and a salt. The heat released in this process is known as the enthalpy of neutralization.

Consider the neutralization of hydrochloric acid (HCl) and sulfuric acid (H₂SO₄) by sodium hydroxide (NaOH). The balanced chemical equations for these neutralizations are:

For the first reaction, each mole of HCl reacts with one mole of NaOH, releasing a certain amount of heat (let's denote this amount by $x$ kJ). For the second reaction, each mole of H₂SO₄ reacts with two moles of NaOH. Since we are given equal volumes and molarities of HCl and H₂SO₄, we can infer that one mole of H₂SO₄ will produce twice the heat of one mole of HCl because it produces double the amount of water.

Thus, the heat evolved in the neutralization of H₂SO₄ by NaOH (denoted as $y$ kJ) will be approximately twice that of HCl.
Therefore, $y = 2x$.

Therefore, the value of $\frac{y}{x}$ is:

So, the value of $\frac{y}{x}$ is 2.