Question Detail

What are the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ?

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 =

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

1. The Diagonals of two squares are in the ratio of 2:5. find the ratio of their areas.

4:25
4:15
3:25
3:15

Answer: Option A

Explanation:

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

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

2. There is a plot which is rectangular in shape and it area is 460 square metres. What will be breadth of the plot if length of plot is 15% more than the breadth of plot ?

8 mtr
10 mtr
15 mtr
20 mtr

Answer: Option D

Explanation:

$\begin{aligned} l*b = 460 m^2 \end{aligned}$ .. (i)
Lets suppose breadth of plot is = b rnLength will be,

$\begin{aligned}l=b*\frac{100+15}{100}\\=\frac{115b}{100}\end{aligned}$ .. (ii)

From (i) and (ii), we get :

$\begin{aligned} \frac{115b}{100}*b = 460 \\ b^2 = \frac{46000}{115} = 400 \\ => b = \sqrt{400} = 20 meter \end{aligned}$

3. The height of an equilateral triangle is 10 cm. find its area.

$\begin{aligned} \frac{120}{\sqrt{3}} cm^2 \end{aligned}$
$\begin{aligned} \frac{110}{\sqrt{3}} cm^2 \end{aligned}$
$\begin{aligned} \frac{100}{\sqrt{3}} cm^2 \end{aligned}$
$\begin{aligned} \frac{90}{\sqrt{3}} cm^2 \end{aligned}$

Answer: Option C

Explanation:

Let each side be a cm, then

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

4. 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

30.68 km/hr
31.68 km/hr
32.68 km/hr
33.68 km/hr

Answer: Option B

Explanation:

In this type of question, we will first calculate the distance covered in given time.
Distance covered will be, Number of revolutions * Circumference

So we will be having distance and time, from which we can calculate the speed. So let solve.

Radius of wheel = 70/2 = 35 cm
Distance covered in 40 revolutions will be

$\begin{aligned} \text{40 * Circumference } \\ = \text{40 * 2*\pi*r } \\ = 40 * 2* \frac{22}{7}* 35 \\ = 8800 cm \\ = \frac{8800}{100} m = 88 m\\ \text{Distance covered in 1 sec =}\\ \frac{88}{10} \\ = 8.8 m \\ Speed = 8.8 m/s \\ = 8.8*\frac{18}{5} = 31.68 km/hr \end{aligned}$

5. One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field.

$\begin{aligned} 120m^2 \end{aligned}$
$\begin{aligned} 130m^2 \end{aligned}$
$\begin{aligned} 140m^2 \end{aligned}$
$\begin{aligned} 150m^2 \end{aligned}$

Answer: Option A

Explanation:

$\begin{aligned} \text{We know }h^2 = b^2+h^2 \\ =>\text{Other side }= \sqrt{(17)^2-(15)^2} \\ = \sqrt{289-225} = \sqrt{64} \\ = 8 meter \\ Area = Length \times Breadth \\ = 15\times8 m^2 = 120 m^2 \end{aligned}$

Question Detail

What are the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ?

1. The Diagonals of two squares are in the ratio of 2:5. find the ratio of their areas.

2. There is a plot which is rectangular in shape and it area is 460 square metres. What will be breadth of the plot if length of plot is 15% more than the breadth of plot ?

3. The height of an equilateral triangle is 10 cm. find its area.

4. 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

5. One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field.

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Question Detail

What are the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ?

1. The Diagonals of two squares are in the ratio of 2:5. find the ratio of their areas.

2. There is a plot which is rectangular in shape and it area is 460 square metres. What will be breadth of the plot if length of plot is 15% more than the breadth of plot ?

3. The height of an equilateral triangle is 10 cm. find its area.

4. 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

5. One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field.

Thanks ! Your comment will be approved shortly !

Videos @mastguru

To Appreciate Our Effort, Please Like Us

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