CAT 2006 — QA Question 4
Basics of Mensuration/PrismEasy
The length, breadth and height of a room are in the ratio 3 : 2 : 1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will
Answer & solution
- A
remain the same.
- B
decrease by 13.64%.
- C
decrease by 15%.
- D
decrease by 18.75%.
decrease by 30%.
Solution
Let the original length, breadth and height of the room be 3x, 2x and x respectively.
∴ The new length, breadth and height are 6x, x and x/2 respectively.
Area of four walls = (2 × length × height) + (2 × breadth × height)
Original area of four walls = 6x2 + 4x2 = 10x2
New area of four walls = 6x2 + x2 = 7x2
∴ Area of wall decreases by [(10x2 − 7x2)/10x2] × 100 = 30%
Hence, option (e).