Question

50 students sat in a classroom and each student requiring 9 m² on floor and 108 m³ in space. If the breadth of the room is 18 m, then find its length and height.

1. 13 m, 25 m
2. 25 m, 12 m
3. 26 m, 12 m
4. 25 m, 13 m

Answer 1

Correct Answer - Option 2 : 25 m, 12 m

Given:

Number of students = 50

The breadth of the room = 18 m

Each student requiring 9 m² on floor

Each student requiring 108 m³ in space

Formula Used:

Area of base of room = L × B

The volume of room = LBH

Where, L = Length, B = Breadth, H = Height

Calculation:

Let the length and height of room be ' L ' meter and "H" meter respectively

Floor area for each student = 9 m²

Floor area for 50 students = 9 × 50

⇒ 9 × 50 = 450 m²

Now, according to the formula 

L × 18 = 450 m² 

⇒ L = 450/18 = 25 m  

Space required for 50 students

⇒ 50 × 108 = 5400 m³

⇒ L × B × H = 5400 m3

⇒ 25 × 18 × H = 5400

⇒ H = 12 m

∴ The length is 25 m and height is 12 m.