Answer: B
Explanation:
\( [3x + \frac {4}{2x + 4}] = \frac {10}{7} \)
\(x = 12 \)
Area of the original rectangle = \( 3x \times 2x = 6xÂ² \)
Area of the original rectangle = \( 6 \times 144 = 864 mÂ² \)
Q2. The perimeter of a rectangle and a square is 160 cm each. If the difference between their areas is 500 cm. If the area of the rectangle is less than that of a Square then find the area of the rectangle?
Answer: C
Explanation:
Perimeter of rectangle = Perimeter of Square = 160
4a = \( 160 \Rightarrow a \) = 40
Area of square = 1600
1600 â€“ lb = 500
lb = 1100 cmÂ²
Q3. Circumference of a circle A is \( \frac {22}{7} \) times perimeter of a square. Area of the square is 441 cmÂ². What is the area of another circle B whose diameter is half the radius of the circle A(in cmÂ²)?
Answer: B
Explanation:
Area = 441 cmÂ²
a = 21 cm
Perimeter of Square = \( 4 \times 21 \)
Circumference of a Circle = \( 4 \times 21 \times \frac {22}{7} \)
2 \( \pi r = 4 \times 3 \times 22 \)
r = \( \frac {12 \times 22 \times 7}{2} \times 22 \) = 42 cm
Radius of Circle B = \( \frac {42}{4} \) = 10.5 cm
Area of Circle = \( \pi rÂ² = \frac {22}{7} \times 10.5 \times 10.5 \) = 346.5 cmÂ²
Q4. The area of a rectangle is equal to the area of a square whose diagonal is \( 12 \sqrt {2} \) meter. The difference between the length and the breadth of the rectangle is 7 meter. What is the perimeter of a rectangle ? (in meter).
Answer: B
Explanation:
d = \( a \sqrt {2} \)
\( 12 \sqrt {2} = a \sqrt {2} \)
a = 12
\( l \times b \) = aÂ² = (12Â²) = 144
l â€“ b = 7
l = b + 7
\( (b + 7) \times (b) \)= 144
bÂ² + 7b â€“ 144 = 0
b = 9
l = 16
2(l + b) = 2(16 + 9) = 50 m
Q5. The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, then the area is increased by 67 square units. Find the area of the rectangle?
Answer: D
Explanation:
Length = \( x \)
Breadth = \( y \)
\( xy â€“ (x5)(y+3) \) = 9
\( 3x â€“ 5y â€“ 6 \)= 0 …………….(i)
\( (x+3)(y+2) â€“ xy \) = 67
\( 2x + 3y 61 \) = 0 …………….(ii)
solving (i) and (ii)
\( x = 17 m \)
\( y = 9 m \)
Area of the Rectangle = 153 m
Answer: D
Explanation:
Area of the plot = \( (4 \times 900) mÂ² \)
= \( 3600 mÂ² \)
Breadth = \( y \) meter
Length = \( 4y\) meter
Now area = \( 4y \times y = 3600 mÂ² \)
\( \Rightarrow yÂ² = 900 mÂ² \)
\( \Rightarrow y = 30 m \)
âˆ´ Length of plot = \( 4y = 120 m \)
Q2. The sum of the radius and height of a cylinder is 19 m. The total surface area of the cylinder is 1672 mÂ², what is the radius and height of the cylinder? (in m)
Answer: D
Explanation:
r + h = 19 m
2 \( \pi r(r + h) \) = 1672
r = \( 1672 \times \frac {7} {2} \times 22 \times 19 \) = 14
r = 14
h = 5
Q3. If each side pair of opposite sides of a square is increased by 20 m, the ratio of the length and breadth of the rectangular so formed becomes 5:3. The area of the old square is?
Answer: B
Explanation:
\( \frac {(x+20)} {x} = \frac {5} {3} \)
\( 3x + 60 = 5x \)
\( x = 30 m \)
Area = \( 900 mÂ² \)
Q4. The length of a park is four times its breadth. A playground whose area is 1024 mÂ² covers 1/4th part of the park. The length of the park is?
Answer: D
Explanation:
l = 4b
Area of the park = \( 4 \times 1024 mÂ² \)
\( l \times b = 4 \times 1024 \)
\( l times \frac {l}{4} = 4 \times 4 \times 1024 \)
\( lÂ² = 1024 \times 16 \)
\( l = 32 \times 4 = 128 m \)
Q5. The width of a rectangular piece of land is \( \frac {1}{{4}{th}} \) of its length. If the perimeter of the piece of land is 320m its length is?
Answer: B
Explanation:
length = \( l \)
breadth = \( \frac {l}{4} \)
\( 2(l + b) \) = 320
\( 2(l + \frac {l}{4}) \) = 320
\( l = 320 \times \frac {4}{10} \) = 128m
Answer: D
Explanation:
Time is taken by a deer to complete one round = 9 minutes
Time is taken by a rabbit to complete one round = 5 minutes
They meet together for the first time at the starting point = LCM of 9 and 5 = 45 minutes.
Q2. A deer and a rabbit can complete a full round on a circular track in 9 minutes and 5 minutes respectively. P, Q, R, and S are the four consecutive points on the circular track which are equidistant from each other. P is opposite to R and Q is opposite to S. After how many minutes will they meet together for the first time when both have started simultaneously from the same point in the same direction(in min)?
Answer: B
Explanation:
Circumference of the track = LCM of 9 and 5 = 45 m.
The ratio of time of deer and rabbit = 9 : 5
The ratio of the speed of deer and rabbit = 5 : 9
Relative Speed = 4 m/min
They meet together for the first time at the starting point = \( \frac {45}{4} \)min
Q3. A cylindrical cistern whose diameter is 14 cm is partly filled with water. If a rectangular block of iron 22 cm in length, 14 cm in breadth and 7 cm in thickness is wholly immersed in water, by how many centimeters will the water level rise?
Answer: B
Explanation:
Volume of the block = \( 22 \times 14 \times 7 \)
Radius of the cistern = \( \frac {14}{2} = 7 \)
Volume of the Cylinder = \( \frac {22}{7} \times R2 \times h \)
\( \frac {22}{7} \times R2 \times h = \frac {22}{7} \times 7 \times 7 \times h \)
\( \frac {22}{7} \times 7 \times 7 \times h = 22 \times 14 \times 7 \Rightarrow h \)= 14
Q4. A well with 28 m inside diameter is dug out 18 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment.
Answer: A
Explanation:
\( \frac {22}{7[(R2) â€“ (r2)]} \times h = \frac {22}{7(7 \times 7 \times 18)} \)
[(352) â€“ (72)] h = \( 14 \times 14 \times 18 \)
\( (42 \times 28) h = 14 \times 14 \times 18 \)
h = 3 m
Q5. The radii of two cylinders are in the ratio 4:5 and their heights are in the ratio 5 : 7, What is the ratio of their curved surface areas?
Answer: B
Explanation:
\( \frac {2 \pi r1 h1}{2 \pi r2 h2} = [\frac {4}{5} \times {5}{7}] \) = 4 : 7
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