A is twice as fast as B and B is thrice as fast as C. The journey covered by C in 78 minutes will be covered by A in-

The ratio of speeds of A, B, C = 6 : 3 : 1
The ratio of time taken by A, B, C = 1/6 : 1/3 : 1
To simplify it, we will multiply it by the LCM of ratio of speeds given.
Hence, the ratio of time taken by A, B, C = 1 : 2 : 6

[Speed is inversely proportional to time, meaning if speed increases, time decreases. So, ratio of time would be reciprocal of the ratio of speed given. ]

Time taken by C to covered given distance = 78 = 6 × 13
The ratio of time of A and C = 1 : 6
Thus, time taken by A = 13 min.

Alternative method:
Let C's speed be x metres/min
Let time taken by A be y min
Then B's speed = 3x metres/min
And, A's speed = 6x metres/min
Ratio of speed of A and C = Ratio of time by C and A
6x : x = 78 : y
6x/x = 78/y
y = 13 min