Introduction
To find the distance between an object and a concave mirror of focal length 40 cm to get an image magnified three times.

Formula Used
The formula used to calculate the distance between an object and a concave mirror is:

1/f = 1/v + 1/u

Where:
f = focal length of the mirror
v = distance of the image from the mirror
u = distance of the object from the mirror

Calculation
To find the distance between an object and a concave mirror of focal length 40 cm to get an image magnified three times, we can use the following steps:

1. Let the distance between the object and the mirror be 'u'.
2. Let the distance between the image and the mirror be 'v'.
3. Since the image is magnified three times, the magnification 'm' is equal to 3.
4. Magnification is given by the formula m = -v/u.
5. Therefore, -v/u = 3.
6. Rearranging the formula, we get v/u = -1/3.
7. Substituting the value of v/u in the formula 1/f = 1/v + 1/u, we get 1/f = -4/3u.
8. Rearranging the formula, we get u = -3f/4.
9. Substituting the value of f as 40 cm, we get u = -30 cm.
10. Since the distance cannot be negative, we take the absolute value of u, which is 30 cm.
11. Therefore, the distance between the object and the concave mirror should be 30 cm.

Conclusion
To get an image magnified three times, the object should be held at a distance of 30 cm from a concave mirror of focal length 40 cm.