For a reaction A + B $\to$products, the rate of the reaction was doubled when the concentration of A was doubled. The rate was also doubled when the concentration of both A and B were doubled. Then, order of the reaction with respect to A and B are :

Let $\mathrm{rate}=\mathrm{k}\left[\mathrm{A}\right]\left[\mathrm{B}\right]$be the equation for the response rate.
The rate doubled when the concentration of A was increased, indicating that the order of the reaction with respect to A is 1.
The order of the reaction with respect to B must be zero because the rate doubled when the concentration of A and B was increased.