Q. A rectangle has an area of 60 square meters and a length of 12 meters. What is the width?
A.
5 meters
B.
6 meters
C.
7 meters
D.
8 meters
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Solution
Area = length × width. Thus, 60 = 12 × width, giving width = 60/12 = 5 meters.
Correct Answer:
B
— 6 meters
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Q. A rectangle's length is 3 times its width. If the area is 75 square meters, what is the length?
A.
15 meters
B.
25 meters
C.
30 meters
D.
20 meters
Show solution
Solution
Let width = x, then length = 3x. Area = length × width = 3x * x = 3x² = 75. Thus, x² = 25, x = 5, and length = 15 meters.
Correct Answer:
A
— 15 meters
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Q. A rectangle's length is three times its width. If the perimeter is 64 cm, what is the area of the rectangle?
A.
192 cm²
B.
128 cm²
C.
96 cm²
D.
64 cm²
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Solution
Let width = x, then length = 3x. Perimeter = 2(length + width) = 2(3x + x) = 8x = 64, so x = 8 cm. Area = length × width = 3x * x = 3(8)(8) = 192 cm².
Correct Answer:
B
— 128 cm²
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Q. A rectangular field is 50 meters long and 30 meters wide. If a fence is built around it, what is the total length of the fence?
A.
160 m
B.
140 m
C.
120 m
D.
180 m
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Solution
Perimeter = 2(length + width) = 2(50 + 30) = 2 × 80 = 160 m.
Correct Answer:
A
— 160 m
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Q. A rectangular garden has a length of 12 m and a width of 5 m. If a path of width 1 m is built around it, what is the area of the path?
A.
50 m²
B.
60 m²
C.
70 m²
D.
80 m²
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Solution
Area of the garden = 12 × 5 = 60 m². Area of the garden with the path = (12 + 2) × (5 + 2) = 14 × 7 = 98 m². Area of the path = 98 - 60 = 38 m².
Correct Answer:
B
— 60 m²
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Q. A rectangular garden has a length of 30 meters and a width of 20 meters. What is the area of the garden?
A.
600 m²
B.
500 m²
C.
400 m²
D.
300 m²
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Solution
Area = length × width = 30 × 20 = 600 m².
Correct Answer:
A
— 600 m²
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Q. A rectangular garden is 10 m long and 6 m wide. If a path of width 1 m is built around it, what is the area of the path? (2023)
A.
32 m²
B.
36 m²
C.
40 m²
D.
44 m²
Show solution
Solution
Area of the garden = 10 * 6 = 60 m². Area including the path = (10 + 2) * (6 + 2) = 12 * 8 = 96 m². Area of the path = 96 - 60 = 36 m².
Correct Answer:
B
— 36 m²
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Q. A rectangular garden is 30 meters long and 20 meters wide. If a path of 1 meter width is built around it, what is the area of the path?
A.
80 m²
B.
100 m²
C.
120 m²
D.
140 m²
Show solution
Solution
Area of the garden = 30 × 20 = 600 m². Area including the path = (30 + 2) × (20 + 2) = 32 × 22 = 704 m². Area of the path = 704 - 600 = 104 m².
Correct Answer:
B
— 100 m²
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Q. A rectangular plot has a length of 50 meters and a width of 30 meters. If a path of 2 meters width is built around it, what is the area of the path?
A.
320 m²
B.
400 m²
C.
600 m²
D.
800 m²
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Solution
Total area with path = (50 + 4) × (30 + 4) = 54 × 34 = 1836 m². Area of the plot = 50 × 30 = 1500 m². Area of the path = 1836 - 1500 = 336 m².
Correct Answer:
B
— 400 m²
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Q. A rectangular prism has dimensions 3 cm, 4 cm, and 5 cm. What is its volume?
A.
60 cm³
B.
12 cm³
C.
15 cm³
D.
20 cm³
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Solution
Volume of a rectangular prism = length × width × height = 3 × 4 × 5 = 60 cm³.
Correct Answer:
A
— 60 cm³
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Q. A rectangular prism has dimensions 3 m, 4 m, and 5 m. What is its surface area?
A.
47 m²
B.
60 m²
C.
70 m²
D.
80 m²
Show solution
Solution
The surface area of a rectangular prism is given by SA = 2(lw + lh + wh). Here, SA = 2(3*4 + 3*5 + 4*5) = 2(12 + 15 + 20) = 2(47) = 94 m².
Correct Answer:
B
— 60 m²
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Q. A rectangular prism has dimensions 4 m, 3 m, and 5 m. What is its surface area?
A.
47 m²
B.
60 m²
C.
70 m²
D.
80 m²
Show solution
Solution
The surface area of a rectangular prism is given by SA = 2(lw + lh + wh). Here, SA = 2(4*3 + 4*5 + 3*5) = 2(12 + 20 + 15) = 2(47) = 94 m².
Correct Answer:
B
— 60 m²
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Q. A rectangular prism has dimensions 4 m, 5 m, and 6 m. What is its surface area?
A.
94 m²
B.
60 m²
C.
70 m²
D.
80 m²
Show solution
Solution
The surface area of a rectangular prism is given by SA = 2(lw + lh + wh). Here, SA = 2(4*5 + 4*6 + 5*6) = 94 m².
Correct Answer:
A
— 94 m²
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Q. A retailer bought a bicycle for $300 and sold it for $360. What is the profit percentage?
A.
15%
B.
20%
C.
25%
D.
30%
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Solution
Profit = Selling Price - Cost Price = $360 - $300 = $60. Profit Percentage = (Profit / Cost Price) * 100 = ($60 / $300) * 100 = 20%.
Correct Answer:
B
— 20%
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Q. A retailer bought a watch for $120 and sold it for $150. What is the profit percentage?
A.
20%
B.
25%
C.
30%
D.
15%
Show solution
Solution
Profit = Selling Price - Cost Price = $150 - $120 = $30. Profit Percentage = (Profit/Cost Price) * 100 = ($30/$120) * 100 = 25%.
Correct Answer:
B
— 25%
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Q. A retailer buys a bicycle for $300 and sells it for $360. What is the profit percentage? (2023)
A.
15%
B.
20%
C.
25%
D.
30%
Show solution
Solution
Profit = Selling Price - Cost Price = 360 - 300 = 60. Profit Percentage = (Profit/Cost Price) * 100 = (60/300) * 100 = 20%.
Correct Answer:
B
— 20%
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Q. A retailer buys a watch for $120 and sells it at a profit of 15%. What is the selling price?
A.
$138
B.
$140
C.
$144
D.
$150
Show solution
Solution
The selling price is calculated as $120 + (15% of $120) = $120 + $18 = $138.
Correct Answer:
C
— $144
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Q. A retailer buys a watch for $150 and sells it at a profit of 25%. What is the selling price? (2023)
A.
$175
B.
$180
C.
$187.5
D.
$200
Show solution
Solution
Selling Price = Cost Price + Profit = 150 + (25% of 150) = 150 + 37.5 = $187.5.
Correct Answer:
C
— $187.5
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Q. A retailer buys a watch for $150 and sells it for $180. What is the profit percentage?
A.
15%
B.
20%
C.
25%
D.
30%
Show solution
Solution
Profit = Selling Price - Cost Price = 180 - 150 = 30. Profit Percentage = (30/150) * 100 = 20%.
Correct Answer:
B
— 20%
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Q. A retailer buys a watch for $300 and sells it at a profit of 15%. What is the selling price?
A.
$345
B.
$350
C.
$360
D.
$375
Show solution
Solution
Selling Price = Cost Price + Profit = $300 + ($300 * 0.15) = $300 + $45 = $345.
Correct Answer:
A
— $345
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Q. A retailer sells a bicycle for $300 after applying a discount of 10%. What was the original price of the bicycle?
A.
$270
B.
$330
C.
$300
D.
$350
Show solution
Solution
Let the original price be x. After a 10% discount, the selling price is x - (0.10 * x) = 0.90x. Setting this equal to $300 gives 0.90x = $300, so x = $300 / 0.90 = $333.33.
Correct Answer:
B
— $330
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Q. A rhombus has diagonals of lengths 12 cm and 16 cm. What is the area of the rhombus?
A.
96 cm²
B.
48 cm²
C.
72 cm²
D.
60 cm²
Show solution
Solution
Area of a rhombus = (1/2) × d1 × d2. Thus, Area = (1/2) × 12 × 16 = 96 cm².
Correct Answer:
A
— 96 cm²
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Q. A seller bought a laptop for $800 and sold it at a loss of 10%. What was the selling price?
A.
$720
B.
$740
C.
$760
D.
$780
Show solution
Solution
Selling Price = Cost Price - Loss = 800 - (10% of 800) = 800 - 80 = $720.
Correct Answer:
A
— $720
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Q. A semicircle has a diameter of 14 cm. What is its area? (Use π ≈ 3.14)
A.
76.96 cm²
B.
48.96 cm²
C.
38.48 cm²
D.
28.96 cm²
Show solution
Solution
Area of a semicircle = (1/2) × πr². Radius = 7 cm. Area = (1/2) × 3.14 × (7)² = 76.96 cm².
Correct Answer:
A
— 76.96 cm²
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Q. A semicircle has a diameter of 14 cm. What is the area of the semicircle?
A.
49 cm²
B.
77 cm²
C.
154 cm²
D.
100 cm²
Show solution
Solution
Area of a semicircle = (1/2) × πr². Radius = 7 cm. Area = (1/2) × 3.14 × (7)² = (1/2) × 3.14 × 49 = 76.96 cm², which rounds to 77 cm².
Correct Answer:
B
— 77 cm²
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Q. A semicircle has a diameter of 14 cm. What is the area of the semicircle? (Use π ≈ 3.14)
A.
76.96 cm²
B.
48.96 cm²
C.
38.48 cm²
D.
24.48 cm²
Show solution
Solution
Area of a semicircle = (1/2) × πr². Radius = 7 cm. Area = (1/2) × 3.14 × (7)² = 76.96 cm².
Correct Answer:
A
— 76.96 cm²
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Q. A semicircle has a diameter of 14 cm. What is the area of the semicircle? (Use π ≈ 22/7)
A.
77 cm²
B.
49 cm²
C.
154 cm²
D.
88 cm²
Show solution
Solution
Radius = 7 cm. Area of semicircle = (1/2) × πr² = (1/2) × (22/7) × (7)² = 77 cm².
Correct Answer:
A
— 77 cm²
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Q. A sequence is defined as 2, 5, 8, 11, ... What is the 15th term of this sequence?
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Solution
The nth term is given by a + (n-1)d. Here, a = 2, d = 3, and n = 15. So, the 15th term = 2 + (15-1) * 3 = 2 + 42 = 44.
Correct Answer:
B
— 41
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Q. A sequence is defined as follows: 2, 5, 8, 11, ... What is the 15th term of this sequence?
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Solution
The first term a = 2 and the common difference d = 3. The 15th term = a + (15-1)d = 2 + 42 = 44.
Correct Answer:
B
— 41
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Q. A sequence of numbers is in arithmetic progression. If the first term is 12 and the last term is 48, and there are 8 terms in total, what is the common difference?
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Solution
The common difference d can be found using the formula for the nth term. The last term is given by a + (n-1)d. Here, 48 = 12 + (8-1)d, solving gives d = 4.
Correct Answer:
A
— 4
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