Question

If the length, breadth and height of the room are in ratio 3:2:1. The breadth and height of the room are halved and length of the room is doubled. Then area of the four walls of the room will,

• A. decrease by 13.64%
• B. decrease by 15%
• C. decrease by 18.75%
• D. decrease by 30%

Hint:

Assign the ratio to a variable k, compute the original wall area with 2(L+B)H, then apply the given changes and compare the two areas.

Answer 1

The Correct Option is D

This can also be verified by plugging in actual numbers instead of keeping the ratio in terms of $k$.

1. Take $k = 2$, so the original dimensions are Length $= 6$, Breadth $= 4$, Height $= 2$ (units), keeping the ratio $3:2:1$.
2. Original wall area $= 2(\text{Length}+\text{Breadth})\times\text{Height} = 2(6+4)\times 2 = 2\times 10\times 2 = 40$.
3. Apply the changes: new Length $= 2\times 6 = 12$, new Breadth $= 4/2 = 2$, new Height $= 2/2 = 1$.
4. New wall area $= 2(12+2)\times 1 = 2\times 14\times 1 = 28$.
5. Percentage change $= \frac{28-40}{40}\times 100 = \frac{-12}{40}\times 100 = -30\%$.

The numeric example gives exactly the same 30% decrease as the general ratio-based method.

\[\boxed{\text{Decrease of } 30\%}\]