Assume there to be some foodstuff that is sufficient for a team for x number of days. After 20 days, 25% of team members happen to quit. It is observed that the remaining foodstuff is sufficient to feed the remaining members for another x number of days. What is the value of x?

Let the initial number of team members be M. The total food available is sufficient for M members for x days, so the initial total food quantity can be represented as M × x units.

After 20 days, the food consumed by M members is 20M units. The remaining food is:
M × x - 20M = M(x - 20)

After 20 days, 25% of the members quit, so the remaining members are 75% of M, which is 0.75M.

The problem states that the remaining food lasts these 0.75M members for another x days. Therefore:
M(x - 20) = 0.75M × x

Dividing both sides by M (assuming M ≠ 0):
x - 20 = 0.75x
x - 0.75x = 20
0.25x = 20
x = 20 / 0.25 = 80