General Questions
Practice and master this topic with our carefully crafted questions.
A typist uses a sheet measuring 20 cm by 30 cm lengthwise .if a margin of 2 cm is left on each side and a 3 cm margin on top and bottom, then percent of the page used for typing is :
Correct Answer: C. 64% ✅
- A. 40% ❌
- B. 60% ❌
- C. 64% ✅ — Correct.
- D. 72% ❌
Explanation:
Original page dimensions = 20 cm × 30 cm
Original area = 20 × 30 = 600 cm²
Margin of 2 cm is left on each side, so usable width:
20 − 2 − 2 = 16 cm
Margin of 3 cm is left on top and bottom, so usable length:
30 − 3 − 3 = 24 cm
Area available for typing:
16 × 24 = 384 cm²
Percentage of page used:
(384 / 600) × 100 = 64%
Exam Fact:
For margin questions, subtract the margins from both sides of each corresponding dimension before calculating the usable area.
Therefore, the correct answer is C. 64% ✅.
A farmer wishes to start a 100 sq. m rectangular vegetable garden. Since he has only 30 m barbed wire, he fences three sides of the garden letting his house compound wall act as the forth side fencing . The dimension of the garden is :
Solution:
Let the length of the garden along the compound wall be l m and the breadth be b m.
The area of the rectangular garden is 100 sq. m.
Area = Length × Breadth
l × b = 100 ...(1)
Since one side is along the house compound wall, fencing is required only for the other three sides.
l + 2b = 30 ...(2)
From equation (2),
l = 30 − 2b
Substituting in equation (1),
(30 − 2b)b = 100
30b − 2b² = 100
b² − 15b + 50 = 0
(b − 5)(b − 10) = 0
b = 5 m or 10 m
If b = 5 m, then
l = 30 − 2 × 5 = 20 m
If b = 10 m, then
l = 30 − 2 × 10 = 10 m
Since the garden is rectangular and the fenced side is usually taken as the longer side, the required dimensions are:
Length = 20 m
Breadth = 5 m
Therefore, the dimensions of the garden are 20 m × 5 m.
Correct Answer: (B) 20 m × 5 m ✅
⚡ Quick Trick:
Fencing is required for only three sides, so:
Length + 2 × Breadth = 30
Check the options whose product is 100:
15 × 6.67 ≈ 100
20 × 5 = 100 ✓
30 × 3.33 ≈ 100
Only 20 + 2 × 5 = 30 satisfies the fencing condition.
A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same is 38cm when folded along the other set of sides. What is the area of the paper ?
Correct Answer: A. 140 cm² ✅
- A. 140 cm² ✅ — Correct.
- B. 240 cm² ❌
- C. 560 cm² ❌
- D. None of these ❌
Explanation:
Let the length of the paper = L and breadth = B.
When folded along one set of sides, the dimensions become L × B/2.
Its perimeter is 34 cm:
2(L + B/2) = 34
2L + B = 34 ...(1)
When folded along the other set of sides, the dimensions become L/2 × B.
Its perimeter is 38 cm:
2(L/2 + B) = 38
L + 2B = 38 ...(2)
From (1):
2L + B = 34
From (2):
L + 2B = 38
Solving:
L = 10 cm, B = 14 cm
Area of the original paper:
L × B = 10 × 14 = 140 cm²
Exam Fact:
When a rectangle is folded into two equal parts, the dimension perpendicular to the fold is halved. Use the resulting dimensions to form the folded rectangle's perimeter.
Therefore, the correct answer is A. 140 cm² ✅.
The diagonal of the floor of a rectangular closet is 7 1/2 feet. The shorter side of the closet 4 1/2 feet. what is the area of the closet in square feet?
Correct Answer: C. 27 ✅
- A. 5 1/4 ❌
- B. 13 1/2 ❌
- C. 27 ✅ — Correct.
- D. 37 ❌
Explanation:
The diagonal of the rectangular closet is 7 1/2 ft and the shorter side is 4 1/2 ft.
Using Pythagoras' theorem:
Diagonal² = Length² + Breadth²
Length² = (7 1/2)² − (4 1/2)²
= (15/2)² − (9/2)²
= 225/4 − 81/4
= 144/4
= 36
Therefore:
Length = 6 ft
Now, area of the closet:
Area = Length × Breadth
= 6 × 4 1/2
= 6 × 4.5
= 27 sq. ft.
Therefore, the area of the closet is 27 square feet.
Exam Fact:
For a rectangle, when the diagonal and one side are given, use Pythagoras' theorem to find the other side, then use Area = Length × Breadth.
Therefore, the correct answer is C. 27 ✅.
A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road ?
Correct Answer: B. 3 m ✅
- A. 2.91 m ❌
- B. 3 m ✅ — Correct.
- C. 5.82 m ❌
- D. None of these ❌
Explanation:
The rectangular park has:
Length = 60 m
Width = 40 m
Area of the park:
60 × 40 = 2400 sq. m
Area of the lawn is 2109 sq. m.
Therefore, the area covered by the two roads is:
2400 − 2109 = 291 sq. m
Let the width of each road be x metres.
The two roads cross each other in the middle, so the overlapping square at the intersection is counted twice. Therefore:
Area of roads = (60 × x) + (40 × x) − x²
291 = 60x + 40x − x²
291 = 100x − x²
Rearranging:
x² − 100x + 291 = 0
(x − 3)(x − 97) = 0
So:
x = 3 m or 97 m
Since the road width cannot be 97 m in a park that is only 40 m wide, we take:
x = 3 m
Therefore, the width of each road is 3 metres.
Exam Fact:
When two roads cross at right angles inside a rectangular area, use:
Area of roads = (Length × road width) + (Breadth × road width) − (road width)²
The intersection is subtracted once because it is otherwise counted twice.
Therefore, the correct answer is B. 3 m ✅.
A park square in shape has a 3 meters wide road inside is running along its sides. The area occupied by the road is 1764 square meters . What is the perimeter along the outer edge of the road ?
Correct Answer: B. 600 m ✅
- A. 576 m ❌
- B. 600 m ✅ — Correct.
- C. 640 m ❌
- D. Data inadequate ❌
- E. None of these ❌
Explanation:
Let the side of the square park be x metres.
The road is 3 m wide along all four sides. Therefore, the side of the inner square is:
x − 3 − 3 = x − 6 m
Area occupied by the road:
Area of outer square − Area of inner square = 1764
x² − (x − 6)² = 1764
x² − (x² − 12x + 36) = 1764
12x − 36 = 1764
12x = 1800
x = 150 m
So, the side of the outer square is 150 m.
The perimeter along the outer edge of the road is:
Perimeter = 4 × side
= 4 × 150
= 600 m
Exam Fact:
For a square with a road of width w running along all four sides:
Road area = x² − (x − 2w)²
Here, the road is 3 m wide, so the inner side is reduced by 6 m.
Therefore, the correct answer is B. 600 m ✅.
The perimeters of five squares are 24cm, 32cm, 40cm, 76cm and 80cm respectively. The perimeter of another square equal in area to the sum of the areas of these squares.
Correct Answer: C. 124 cm ✅
- A. 31 cm ❌
- B. 62 cm ❌
- C. 124 cm ✅ — Correct.
- D. 961 cm ❌
Explanation:
For a square:
Side = Perimeter ÷ 4
So the sides of the five squares are:
24 ÷ 4 = 6 cm
32 ÷ 4 = 8 cm
40 ÷ 4 = 10 cm
76 ÷ 4 = 19 cm
80 ÷ 4 = 20 cm
Their total area:
= 6² + 8² + 10² + 19² + 20²
= 36 + 64 + 100 + 361 + 400
= 961 cm²
Therefore, the side of the new square:
= √961 = 31 cm
Perimeter of the new square:
= 4 × 31
= 124 cm
Exam Fact:
When a new square has an area equal to the sum of several square areas, first find the total area, then take its square root to get the new side.
Therefore, the correct answer is C. 124 cm ✅.
The perimeter of square is 48cm. The area of a rectangle is 4 cm² less than the area of the square. If the length of the rectangle is 14cm, then its perimeter is :
Correct Answer: D. 48 cm ✅
- A. 40 cm ❌
- B. 44 cm ❌
- C. 46 cm ❌
- D. 48 cm ✅ — Correct.
Explanation:
Perimeter of square = 48 cm
Side of square = 48 ÷ 4 = 12 cm
Area of square = 12 × 12 = 144 cm²
Area of rectangle = 144 − 4 = 140 cm²
Length of rectangle = 14 cm
Breadth = 140 ÷ 14 = 10 cm
Perimeter of rectangle:
= 2(14 + 10)
= 2 × 24
= 48 cm
Quick Check:
14 × 10 = 140 cm², which is exactly 4 cm² less than the square's 144 cm².
Exam Fact:
Always calculate the square's side first from its perimeter, then use the area difference to find the rectangle's breadth.
Therefore, the correct answer is D. 48 cm ✅.
What will be the length of the diagonal of that square plot whose area is equal to the area of a rectangle to that of a square whose side is equal to the breadth of the rectangle ?
Correct Answer: C. Data inadequate ✅
- A. 42.5 m ❌
- B. 60 m ❌
- C. Data inadequate ✅ — Correct.
- D. None of these ❌
Explanation:
Let the length of the rectangle = L and breadth = B.
Area of rectangle = L × B
Area of the square whose side equals the breadth = B²
If the required square plot has an area equal to the combined area of these two:
Required area = LB + B² = B(L + B)
To find the diagonal of the required square, we need the actual values of L and B. These values are not given in the question.
Therefore, a numerical diagonal such as 42.5 m or 60 m cannot be determined.
Exam Fact:
When the dimensions or sufficient numerical information are missing, a unique numerical answer cannot be calculated. In such cases, choose Data inadequate.
Therefore, the correct answer is C. Data inadequate ✅.
What is the least number of square titles required to pave the floor of a room 15m 17cm long and 9 m 2 cm broad ?
Correct Answer: A. 814 ✅
- A. 814 ✅ — Correct.
- B. 820 ❌
- C. 840 ❌
- D. 844 ❌
Explanation:
Length of the room = 15 m 17 cm = 1517 cm
Breadth of the room = 9 m 2 cm = 902 cm
For the least number of square tiles, the side of the largest square tile must be the HCF of the length and breadth.
HCF of 1517 and 902:
1517 − 902 = 615
902 − 615 = 287
615 − 2(287) = 41
287 ÷ 41 = 7
Therefore, HCF = 41 cm.
So, side of each square tile = 41 cm.
Number of tiles along the length:
1517 ÷ 41 = 37
Number of tiles along the breadth:
902 ÷ 41 = 22
Total number of tiles:
37 × 22 = 814
Exam Fact:
To find the least number of square tiles needed to cover a rectangular floor, find the HCF of the length and breadth. This gives the side of the largest possible square tile.
Therefore, the correct answer is A. 814 ✅.