SECTION – 5

110. A ladder 25 meters long is placed against a wall with its foot 7 meters away from the foot of the wall. How far should the foot be drawn out so that the top of the ladder may come down by half the distance of the total distance if the foot is drawn out?

(A) 6 meters (B) 8 meters (C) 8.75 meters (D) None of the above

Solution:

The initial position of the ladder is shown in the figure below, on the left.

The wording is not very clear. “………, so that the top of the ladder may come down by half the distance of the total distance IF the foot is drawn out.”

If the foot is drawn out (until the ladder is flat on the ground) by 18 m, the top of the ladder comes down by 24 m. If it comes down by half of this distance, i.e. by 12 m, the position of the ladder is shown in the figure on the right.

If the top of the ladder slides to C, bottom of the ladder slides to D.

where OD =

\ BD » 22 – 7 = 15

Instead of the word IF, if we have the word THAT we get the following conclusion. Let the foot be drawn out by 2x m. The top slides down by x m. \ (24 – x)² + (7+ 2x)² = 625 Þ x = 0 or 4. The foot should be drawn out by 0 m or 8 m.

It is probable that this may have been the intended question. But the key word that was printed is IF and not THAT. Therefore we have more reason to accept 15 or choice D as our answer. Choice (D)