There are two jars of sweets.

If 20 are taken from the first jar and put into the second, they are in the ratio of 1:2

If 60 are now taken from the second and put into the first, they are in the ratio of 3:1

Work out the original amount in each.

First, we model two equations that satisfy the problem. Let x be the number of sweets in the first jar, and y the number of sweets in the second jar.

First equation:

(x-20) / 1 = (y+20) / 2

or

(x-20) / (y+20) = 1/2

Second equation:

[ (x-20) + 60]/3 = [ (y+20) - 60]/1

or

(x+40) = 3 (y-40)

Expressing the first equation in terms of y, we have:

y = 2x - 60

Plugging it in to the second equation:

(x+40) = 3[ (2x-60) - 40]

5x = 340

x = 68

y = 2 (68) - 60 = 76

The first jar originally had 68 sweets and the second jar originally had 76 sweets.