50 square stone slabs of equal size were needed to cover a floor area of 72 sq.m. Find the length of each stone slab.

Answer: Option D

Explanation:

Let original length = x
and original width = y
Decrease in area will be
$$\begin{aligned} = xy-\left( \frac{80x}{100}\times\frac{90y}{100}\right) \\ = \left(xy- \frac{18}{25}xy\right) \\ = \frac{7}{25}xy \\ \text{Decrease = }\left(\frac{7xy}{25xy} \times100\right) \% \\ = 28\% \end{aligned}$$

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:

$$\begin{aligned} \text{Area of Square =} \pi*r^2\\ => \pi*r^2 = 24.64 \\ => r^2 = \frac{24.64}{22}*7 \\ => r^2 = 7.84 \\ => r = \sqrt{7.84} \\ => r = 2.8 \\ \text{Circumference =}2\pi*r\\ = 2*\frac{22}{7}*2.8 \\ = 17.60m \end{aligned}$$

Answer: Option D

Explanation:

Area of each slab =
$$\begin{aligned} \frac{72}{50}m^2 = 1.44 m^2\\ \text{Length of each slab =}\sqrt{1.44} \\ = 1.2m = 120 cm \end{aligned}$$

Answer: Option D

Explanation:

If area is given then we can easily find side of a square as,
$$\begin{aligned}Side = \sqrt{69696} \\ = 264 cm \\ \text{we know diagonal =}\sqrt{2}\times side \\ = \sqrt{2}\times 264 \\ = 1.414 \times 264 \\ = 373.296 cm \end{aligned}$$