M4maths Previous Puzzles

19 Sep 2022 Area & Volume

Length, breadth and height of a room are in the ratio 6:5:3. If a new room is constructed where length is increased by 40%, breadth by 20% but the area of all four wall is kept same as original room, then change in volume of a new room compared to original is

OPtion

1) 28.80%
2) 21.66%
3) 14.40%
4) 33.66%
5) 14.33%
6) 21.40%
7) 15.20%
8) 30.66%
9) 28.33%
10) None of these

Solution

For the original room, let Length=6, Breadth=5 and Height=3, then its area of 4 walls=2(6*3 + 5*3)=66 unit² and Volume=6*5*3=90 unit³
For a new room, Length=1.4*6=8.4, Breadth=1.2*5=6. If height is 'x' then area of 4 walls=2(8.4x + 6x)=28.8x unit²
As the area of walls of both rooms is same .'. 28.8x=66 ⇒ x=165/72
So, the volume of new room=8.4*6*(165/72)=115.5 unit³
Hence percentage increase in volume=[(115.5-90)/90]*100=28.33%
Correct Option 9)

Correct Option: 9 Best Solution (0)