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Question Detail
What will be the cost of gardening 1 meter boundary around a rectangular plot having perimeter of 340 meters at the rate of Rs. 10 per square meter ?
- Rs. 3430
- Rs. 3440
- Rs. 3450
- Rs. 3460
Answer: Option B
Explanation:
In this question, we are having perimeter.
We know Perimeter = 2(l+b), right
So,
2(l+b) = 340
As we have to make 1 meter boundary around this, so
Area of boundary = ((l+2)+(b+2)-lb)
= 2(l+b)+4 = 340+4 = 344
So required cost will be = 344 * 10 = 3440
1. 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.
- 110 cm
- 116 cm
- 118 cm
- 120 cm
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}
2. 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}
3. The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
- 32%
- 34%
- 42%
- 44%
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}
4. If the area of a square with the side a is equal to the area of a triangle with base a, then the altitude of the triangle is.
- a
- a/2
- 2a
- None of above
Answer: Option C
Explanation:
\begin{aligned}
\text{We know area of square =}a^2 \\
\text{Area of triangle =}\frac{1}{2}*a*h \\
=> \frac{1}{2}*a*h = a^2 \\
=> h = 2a
\end{aligned}
5. 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}
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