The wheel of a motorcycle, 70 cm in diameter makes 40 revolutions in every 10 seconds. What is the speed of the motorcycle in km/hr

Answer: Option A

Explanation:

Let the diagonals of the squares be 2x and 5x.
Then ratio of their areas will be

$$\begin{aligned} \text{Area of square} = \frac{1}{2}*{Diagonal}^2 \\ \frac{1}{2}*{2x}^2:\frac{1}{2}*{5x}^2 \\ 4x^2:25x^2 = 4:25 \end{aligned}$$

Answer: Option B

Explanation:

In this type of questions, first we need to calculate the area of tiles. With we can get by obtaining the length of largest tile.
Length of largest tile can be obtained from HCF of length and breadth.
So lets solve this,

Length of largest tile = HCF of (1517 cm and 902 cm)
= 41 cm

Required number of tiles =

$$\begin{aligned} \frac{\text{Area of floor}}{\text{Area of tile}} \\ = \left(\frac{1517\times902}{41 \times 41}\right)\\ = 814 \end{aligned}$$

Answer: Option A

Explanation:

Let the triangle and parallelogram have common base b,
let the Altitude of triangle is h1 and of parallelogram is h2(which is equal to 100 m), then

$$\begin{aligned} \text{Area of triangle =}\frac{1}{2}*b*h1\\ \text{Area of rectangle =}b*h2\\ \text{As per question }\\ \frac{1}{2}*b*h1 = b*h2 \\ \frac{1}{2}*b*h1 = b*100 \\ h1 = 100*2 = 200 m \\ \end{aligned}$$

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:

Let each side be a cm, then

$$\begin{aligned} \left(\frac{a}{2}\right)^2+{10}^2 = a^2 \\ <=>\left(a^2-\frac{a^2}{4}\right) = 100 \\ <=> \frac{3a^2}{4} = 100 \\ a^2 = \frac{400}{3} \\ Area = \frac{\sqrt{3}}{4}*a^2 \\ = \left(\frac{\sqrt{3}}{4}*\frac{400}{3}\right)cm^2 \\ = \frac{100}{\sqrt{3}}cm^2 \end{aligned}$$