-
The length, breadth and height of a cuboid are in the ratio 1 : 2 : 3. If they are increased by 100%, 200% and 200% respectively, then compared to the original volume the increase in the volume of the cuboid will be
-
- 5 times
- 18 times
- 12 times
- 17 times
- 5 times
Correct Option: D
Let length, breadth and height of a cuboid are increased by x%, y% and z% respectively, then its volume is increased by
 | x + y + z + | + |  | % | |||
| 100 | 10000 |
| ∴ Effective increase = | | 100 + 200 + 20000 + 40000 + | + | | % | ||
| 100 | 10000 |
= 500 + 800 + 400 = 1700 %
| = 1700 × | = 17 times | |
| 100 |
Method : 2
Original volume = x × 2x × 3x = 6x³ cubic units
New volume = 2x × 6x × 9x = 108x³ cubic units
Change in volume = 108x³ – 6x³ = 102x³ cubic units
| Increase = | = 17 times | |
| 6x³ |
