UPSC CDS 1 2020 Math Paper

Concept:The ladder forms right triangles with each wall and the floor. The base of the ladder remains fixed, so the distances from the base to each wall add up to the room's breadth.Explanation:Let the foot of the ladder be at a fixed point on the floor.When the ladder reaches a height of $4.8$ m on one wall, let the distance from the foot to that wall be $x$ m.Using Pythagoras theorem: $5^2 = 4.8^2 + x^2$.$x^2 = 25 - 23.04 = 1.96$, so $x = \sqrt{1.96} = 1.4$ m.When the ladder is turned to the opposite wall, it reaches a height of $1.4$ m. Let the distance from the foot to that wall be $y$ m.Again, $5^2 = 1.4^2 + y^2$.$y^2 = 25 - 1.96 = 23.04$, so $y = \sqrt{23.04} = 4.8$ m.The breadth of the room is the total distance between the two walls, which is $x + y = 1.4 + 4.8 = 6.2$ m.Answer:$6.2$ m (Option C).