By what factor would a person's weight be increased if Earth had 10 times its present mass, but the same volume?

10 times

Explanation:

The weight of the person is defined as the product of mass of person and the acceleration due to gravity of that planet.

Let the gravity is g.

W = m x g ... (1)

Now the value of g depends on the mass of earth when the radius of earth is constant.

g' = 10 g

So, W' = m x g' = m x 10 g = 10 mg = 10 W (from (1)

So, the weight of the person becomes 10 times.