Hello,

Assume the length of the spring to be 'l'

Now the ratios of lengths in which the spring is cut is 1:2:3

That means the length of the three new springs will be x, 2x and 3x where x is equal to some constant.

Therefore, 1x + 2x + 3x = l

= 6x = l

= x = l/6

Now length of new springs will be l/6, 2l/6 and 3l/6

(Substituting the value of x = l/6)

Hope it is clear now.