The area of a rectangle is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the rectangular field ?

Answer: Option D

Explanation:

As far as questions of Area or Volume and Surface area are concerned, it is all about formulas and very little logic. So its a sincere advice to get all formulas remembered before solving these questions.

Lets solve this,

$$\begin{aligned} \text{Area of rectangle =}l*b\\ \text{Area of triangle =}\frac{1}{2}l*b\\ \text{Ratio =}l*b:\frac{1}{2}l*b \\ = 1:\frac{1}{2} \\ = 2:1 \end{aligned}$$

One little thing which should be taken care in this type of question is, be sure you are calculating ration in the given order of the question.
If it is ratio of triangle and rectangle then we have to write triangle formula first. cheers :)

Answer: Option D

Explanation:

Let original length = x metres and original breadth = y metres.

$$\begin{aligned} \text{Original area } = \text{xy } m^2 \\ \text{New Length }= \frac{120}{100}x = \frac{6}{5}x \\ \text{New Breadth }= \frac{120}{100}y = \frac{6}{5}y \\ =>\text{New Area }= \frac{6}{5}x * \frac{6}{5}y \\ =>\text{New Area }= \frac{36}{25}xy \\ \text{Area Difference} = \frac{36}{25}xy - xy \\ = \frac{11}{25}xy \\ Increase \% = \frac{Differnce}{Actual}*100 \\ = \frac{11xy}{25}*\frac{1}{xy}*100 = 44\% \end{aligned}$$

Answer: Option C

Explanation:

Let Breadth = x cm,
then, Length = 3x cm
$$\begin{aligned} x^2+{(3x)}^2 = {(8\sqrt{10})}^2 \\ => 10x^2 = 640 \\ => x = 8 \\ \end{aligned}$$
So, length = 24 cm and breadth = 8 cm
Perimeter = 2(l+b)
= 2(24+8) = 64 cm

Answer: Option C

Explanation:

Let the original radius be R cm. New radius = 2R

$$\begin{aligned} Area = \pi R^2 \\ \text{New Area =} \pi {2R}^2 \\ = 4\pi R^2 \\ \text{Increase in area =}(4\pi R^2 - \pi R^2) \\ = 3\pi R^2 \\ \text{Increase percent =} \frac{3\pi R^2}{\pi R^2}*100 \\ = 300 \% \end{aligned}$$

Answer: Option A

Explanation:

$$\begin{aligned} 2\pi R1 = 4 \pi \\ => R1 = 2 \\ 2\pi R2 = 8 \pi \\ => R2 = 4 \\ \text{Original Area =} 4\pi * 2^2 \\ = 16 \pi \\ \text{New Area =} 4\pi * 4^2 \\ = 64 \pi \end{aligned}$$

So the area quadruples.