Given:
- The image obtained by a convex lens is erect.
- The length of the image is four times the length of the object.
- The focal length of the convex lens is 20 cm.

To Find:
- Object distance (u)
- Image distance (v)

Formula:
The magnification produced by a lens is given by the formula:
magnification (m) = -v/u

The length of the image (I') is related to the length of the object (O) and the magnification (m) by the formula:
I'/O = -m

Solution:
Let's solve the problem step by step:

Step 1: Determine the magnification (m):
Given that the length of the image (I') is four times the length of the object (O), we can write:
I'/O = 4

Since the image is erect, the magnification (m) is positive:
m = I'/O = 4

Step 2: Calculate the object distance (u):
Using the magnification formula, we have:
m = -v/u

Substituting the given value of magnification:
4 = -v/u

Step 3: Calculate the image distance (v):
We know that the focal length (f) of the convex lens is 20 cm. By using the lens formula:
1/f = 1/v - 1/u

Substituting the given value of focal length:
1/20 = 1/v - 1/u

Since we have the equation 4 = -v/u from Step 2, we can substitute -v/u for 4 in the lens formula:
1/20 = 1/v - 1/(-v/4)

Simplifying the equation:
1/20 = 1/v + 4/v

Combining the fractions:
1/20 = (1 + 4)/v

Simplifying further:
1/20 = 5/v

Cross-multiplying:
v = 100 cm

Step 4: Calculate the object distance (u):
Using the equation 4 = -v/u from Step 2, we can substitute the value of v:
4 = -100/u

Solving for u:
u = -100/4
u = -25 cm

However, since the object distance (u) should be positive for a real object, we take the absolute value:
u = 25 cm

Answer:
The object distance (u) is 25 cm and the image distance (v) is 100 cm.