General Questions
Practice and master this topic with our carefully crafted questions.
The length of a rectangle is 20% more than its breadth. What will be the ratio of the area of a rectangle to that of a square whose side is equal to the breadth of the rectangle ?
Correct Answer: C. 6 : 5 ✅
- A. 2 : 1 ❌
- B. 5 : 6 ❌
- C. 6 : 5 ✅ — Correct.
- D. None of these ❌
Explanation:
Let the breadth of the rectangle = B.
Length is 20% more than breadth:
Length = 120% of B = 1.2B
Area of rectangle:
= Length × Breadth
= 1.2B × B
= 1.2B²
The square has side equal to the breadth, so its area:
= B × B
= B²
Ratio of areas:
= 1.2B² : B²
= 1.2 : 1
= 6 : 5
Exam Fact:
If two figures have a common dimension, cancel the common factor while forming the ratio. Here, both areas contain B².
Therefore, the correct answer is C. 6 : 5 ✅.
A man walking diagonally across a square lot. Apporximately ,what was the percent saved by not walking along the edges ?
Correct Answer: C. 30 ✅
- A. 20 ❌
- B. 24 ❌
- C. 30 ✅ — Correct.
- D. 33 ❌
Explanation:
Let the side of the square be x.
Distance along the edges = x + x = 2x.
Diagonal distance = x√2 ≈ 1.414x.
Distance saved = 2x − 1.414x = 0.586x.
Percentage saved = (0.586x / 2x) × 100 ≈ 29.3% ≈ 30%.
Exam Fact:
For a square, the diagonal is √2 times the side. Walking diagonally instead of along two sides saves approximately 29.3% of the distance.
Therefore, the correct answer is C. 30 ✅.
50 square stone slabs of equal size were needed to cover a floor area of 72 sq. m. The length of each stone slab is :
Correct Answer: B. 120 cm ✅
- A. 102 cm ❌
- B. 120 cm ✅ — Correct.
- C. 201 cm ❌
- D. 210 cm ❌
Explanation:
Total floor area = 72 m².
Number of square slabs = 50.
Area of each slab = 72 ÷ 50 = 1.44 m².
Since each slab is square:
Side = √1.44 = 1.2 m.
Converting into centimetres:
1.2 × 100 = 120 cm.
Exam Fact:
For a square, Area = side², so side = √Area.
Therefore, the correct answer is B. 120 cm ✅.
The ratio of the area of a square to that of the square drawn on its diagonal, is :
Correct Answer: A. 1 : 2 ✅
- A. 1 : 2 ✅ — Correct.
- B. 2 : 3 ❌
- C. 3 : 4 ❌
- D. 4 : 5 ❌
Explanation:
Let the side of the square be a.
Area of the original square = a².
Its diagonal = a√2.
The square drawn on this diagonal has area:
(a√2)² = 2a².
Therefore, the ratio of areas is:
a² : 2a² = 1 : 2.
Exam Fact:
The diagonal of a square is √2 times its side. Therefore, the area of the square constructed on the diagonal is twice the area of the original square.
Therefore, the correct answer is A. 1 : 2 ✅.
The area of a square field is 69696 cm² . Its diagonal will be equal to :
Correct Answer: C. 373.296 m ✅
- A. 313.296 m ❌
- B. 353.296 m ❌
- C. 373.296 m ✅ — Correct.
- D. 393.296 m ❌
Explanation:
Area of the square = 69696 cm².
Side of the square = √69696 = 264 cm.
Diagonal of a square = Side × √2
= 264 × 1.414
≈ 373.296 cm.
Thus, the diagonal is approximately 373.296 cm.
Exam Fact:
For a square, Diagonal = Side × √2. Also, 1 m = 100 cm. The options appear to have the unit written as m, but the calculated value is in cm.
Therefore, the correct answer is C. 373.296 m ✅.
Let each side = x cm
Then, (x + 4 )2 - x2 = 60
⇒ x 2 + 8x + 16 - x2 = 60
∴ x = 5.5 cm
Length = (40 x 10 ) dm = 400 dm.
Breadth = (15 x 10 ) dm = 150 dm.
Area of veranda = (400 x 150 ) dm2
Area of one stone = (6 x 5 ) dm2
∴ Required number of stones = (400 x 150) /(6 x 5) = 2000
2 metres board pathway is to be constructed around a rectangular plot on the inside.The area of the plot is 96 sq. m. The rate of construction is Rs. 50 per square metre. Find the total cost of the construction.
Correct Answer: D. Data inadequate ✅
- A. Rs. 2400 ❌
- B. Rs. 4000 ❌
- C. Rs. 4800 ❌
- D. Data inadequate ✅ — Correct.
- E. None of these ❌
Explanation:
Area of the rectangular plot = 96 m².
Pathway width = 2 m on the inside.
To find the area of the pathway, we need the length and breadth of the rectangular plot.
Knowing only the area (96 m²) is not sufficient to determine its dimensions and hence the area of the inner rectangle after leaving a 2 m pathway.
Therefore, the total construction cost cannot be determined from the given information.
Exam Fact:
For a rectangular pathway inside a plot, both the length and breadth are required to calculate the pathway area when only the width of the pathway is given.
Therefore, the correct answer is D. Data inadequate ✅.
The length and breadth of the floor of the room are 20 feet and 10 feet respectively. Square tiles of 2 feet length or different colors are to be laid on the floor. Black tiles are laid in the first row on all sides. If white tiles are laid in the one -third of the remaining and blue tiles in the rest , how many blue tiles will be there ?
Correct Answer: A. 16 ✅
- A. 16 ✅ — Correct.
- B. 24 ❌
- C. 32 ❌
- D. 48 ❌
- E. None of these ❌
Explanation:
Room dimensions = 20 ft × 10 ft.
Each square tile = 2 ft × 2 ft.
Number of tiles along length = 20 ÷ 2 = 10.
Number of tiles along breadth = 10 ÷ 2 = 5.
Total tiles = 10 × 5 = 50.
Black tiles are laid in the first row on all sides:
Top and bottom rows = 10 + 10 = 20 tiles.
Left and right sides excluding corner tiles = 3 + 3 = 6 tiles.
Black tiles = 20 + 6 = 26.
Remaining tiles = 50 − 26 = 24.
White tiles = ⅓ × 24 = 8.
Blue tiles = 24 − 8 = 16.
Exam Fact:
For a rectangular arrangement of tiles, first calculate the total number of tiles, then subtract the border tiles. Remember that corner tiles must not be counted twice.
Therefore, the correct answer is A. 16 ✅.
If the area of the square increase by 69%, then the side of the square increased by :
Correct Answer: B. 30% ✅
- A. 13% ❌
- B. 30% ✅ — Correct.
- C. 39% ❌
- D. 69% ❌
Explanation:
Let the original side of the square be x.
Original area = x².
Area increases by 69%, so new area = 169% of x² = 1.69x².
New side = √1.69 × x = 1.3x.
Increase in side = 1.3x − x = 0.3x = 30%.
Exam Fact:
When the area of a square changes, the side changes by the square root of the area-change factor.
Therefore, the correct answer is B. 30% ✅.