4/7 of a pole is in the mud. When one-third of this submerged portion is…

When a known fraction of a whole is inside the mud and a further fraction of that submerged part is then removed, the length still buried equals (1 minus the removed fraction) times the submerged fraction times the total length. Equating this remaining buried length to the value given in the problem produces a straightforward linear equation in the unknown total length.

1. Let the total length of the pole be L metres.

2. The portion of the pole in the mud = (4/7)L.

3. Pulling out one third of this submerged portion leaves two-thirds of it still buried.

4. Remaining buried length = (2/3) x (4/7)L = (8/21)L.

5. This remaining length equals 8 m, so (8/21)L = 8.

6. Solving: L = 8 x (21/8) = 21 metres.

Check: with L = 21 m, the submerged part is (4/7) x 21 = 12 m. Removing one third of 12 m takes away 4 m, leaving 12 minus 4 = 8 m still in the mud, exactly matching the given condition, so the total length of the pole is 21 metres.