The distance travelled with M is 12 km

K, L & M are three persons. First K walks with L and then with M.

Let the time taken by K when walking with L be x hr and time taken by K when walking with M be y hr

Then,

Total time taken by K = 7 hr...

⇒x + y = 7...(1)

x + y = 7

Again,

Distance travelled by K with L = 3x (∵ Distance = $$Speed\times Time$$)

Similarly, distance travelled by K with M = 6y

Total distance travelled by K = 27 km

⇒3x + 6y = 27

x + 2y = 9....(2)

3x + 6y = 27

x + 2y = 9

Subtracting eq (1) from eq (2)

We get, y = 2

Thus, the distance travelled by K with M = $$2\times 6$$ = 12 km