Answer
$P_{He}=7.00\times P_{N_{2}}$
Work Step by Step
Density $d= \frac{PM}{RT}$ where P is the pressure, M is the molar mass, R is the universal gas constant and T the temperature.
As densities are equal, we have
$\frac{P_{He}M_{He}}{RT}=\frac{P_{N_{2}}M_{N_{2}}}{RT}$ (temperature for both the gases are equal)
$\implies P_{He}M_{He}=P_{N_{2}}M_{N_{2}}$
As $M_{He}= 4.00\,g/mol$ and
$M_{N_{2}}=28.0\,g/mol$, we get
$P_{He}\times4.00\,g/mol=P_{N_{2}}\times28.0\,g/mol$
Or $P_{He}=7.00\times P_{N_{2}}$
