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Question Detail
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}
1. 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}
2. If the ratio of the areas of two squares is 225:256, then the ratio of their perimeters is :
- 15:12
- 15:14
- 15:16
- 15:22
Answer: Option C
Explanation:
\begin{aligned}
\frac{a^2}{b^2} = \frac{225}{256} \\
\frac{15}{16} \\
<=> \frac{4a}{4b} = \frac{4*15}{4*16} \\
= \frac{15}{16} = 15:16
\end{aligned}
3. The sides of a triangle are in the ratio of \begin{aligned}\frac{1}{2}:\frac{1}{3}:\frac{1}{4}\end{aligned}. If the perimeter is 52 cm, then find the length of the smallest side.
- 12 cm
- 14 cm
- 16 cm
- 18 cm
Answer: Option A
Explanation:
\begin{aligned}
\text{Ratio of sides =}\frac{1}{2}:\frac{1}{3}:\frac{1}{4} \\
=6:4:3\\
Perimeter = 52 cm \\
\text{So sides are =} \\
\left( 52*\frac{6}{13}\right)cm,\left( 52*\frac{4}{13}\right)cm, \left( 52*\frac{3}{13}\right)cm
\end{aligned}
a = 24 cm, b = 16 cm and c = 12 cm
Length of the smallest side = 12 cm
4. The base of a triangle is 15 cm and height is 12 cm. The height of another triangle of double the area having the base 20 cm is :
- 22 cm
- 20 cm
- 18 cm
- 10 cm
Answer: Option C
Explanation:
\begin{aligned}
\text{Area of triangle, A1 = }\frac{1}{2}*base*height \\
= \frac{1}{2}*15*12 = 90 cm^2 \\
\text{Area of second triangle =} 2*A1 \\
= 180 cm^2 \\
\frac{1}{2}*20*height = 180 \\
=> height = 18 cm
\end{aligned}
5. 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 ?
- 714
- 814
- 850
- 866
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}
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