To solve this problem, we can use the concept of proportions.

Let's assume that the amount of rice stored is represented by "x" and the number of days it can feed 90 people is represented by "y".

According to the given information, we have the following proportion:

x/90 = y/21

Now, we need to find the new number of days (represented by "z") when the number of people decreases to 60. We can set up a new proportion using the same amount of rice stored:

x/60 = z/21

To find the value of "z", we can cross-multiply and solve for "z":

60z = 21x

Dividing both sides by 21:

z = (60/21) * x
z = 20/7 * x

So, the amount of rice stored will last for (20/7) times the number of days it originally lasted for 90 people.

To find the number of days the amount of rice stored will increase, we can subtract the original number of days from the new number of days:

Increase in days = z - y
Increase in days = (20/7 * x) - y

Please note that we need the value of "x" (the amount of rice stored) to calculate the increase in days accurately.