General Questions
Practice and master this topic with our carefully crafted questions.
The area of a rectangle is 460 square metres. if the length is 15% more than the breadth, what is the breadth of the rectangular field ?
Solution:
Let the breadth of the rectangle be x metres.
Since the length is 15% more than the breadth,
Length = x + 15% of x
= x + 0.15x
= 1.15x
Given:
Area = Length × Breadth
460 = 1.15x × x
460 = 1.15x²
Solving for x:
x² = 460 ÷ 1.15
x² = 400
x = √400
x = 20 metres
Therefore, Breadth = 20 metres.
Since 20 metres is not given in the options,
Correct Answer: (E) None of these ✅
⚡ Quick Trick:
If length is 15% more than breadth, then:
Area = 1.15 × Breadth²
Breadth² = 460 ÷ 1.15 = 400
Breadth = √400 = 20 metres
The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of ₹800 per sq. metre.
Solution:
Given that the length of the room is 5.5 m and the width is 3.75 m.
First, find the area of the floor.
Area of floor = Length × Width
= 5.5 × 3.75
= 20.625 sq. m
The cost of paving is ₹800 per sq. metre.
Total Cost = Area × Rate
= 20.625 × 800
= ₹16,500
Therefore, the cost of paving the floor is ₹16,500.
Correct Answer: (D) ₹16,500 ✅
⚡ Quick Trick:
To find the cost of paving, directly use:
Cost = Length × Width × Rate
= 5.5 × 3.75 × 800
= 20.625 × 800
= ₹16,500
Hence, the required cost = ₹16,500
The difference between length and breadth of a rectangle is 23 m. if its perimeter is 206 m, then its area is :
Solution:
Let the length of the rectangle be l metres and the breadth be b metres.
Given that the difference between length and breadth is 23 m.
l − b = 23
The perimeter of the rectangle is 206 m.
2(l + b) = 206
l + b = 103
Now, solving the two equations:
l + b = 103
l − b = 23
Adding both equations:
2l = 126
l = 63 m
b = 103 − 63
= 40 m
Hence, the area of the rectangle is:
Area = Length × Breadth
= 63 × 40
= 2520 m²
Therefore, the area of the rectangle is 2520 m².
Correct Answer: (D) 2520 m² ✅
⚡ Quick Trick:
When the sum and difference of two numbers are known:
Length = (Sum + Difference) ÷ 2
= (103 + 23) ÷ 2
= 63 m
Breadth = (Sum − Difference) ÷ 2
= (103 − 23) ÷ 2
= 40 m
Area = 63 × 40 = 2520 m²
If the area of a rectangular plot increases by 30% while its breadth remains same, what will be the ratio of the area of new and old figures ?
Solution:
Let the old area of the rectangular plot be 100 units.
The area increases by 30% while the breadth remains the same.
New Area = 100 + 30% of 100
= 100 + 30
= 130 units
Therefore, the ratio of the new area to the old area is:
New Area : Old Area
= 130 : 100
= 13 : 10
Therefore, the required ratio is 13 : 10.
Since 13 : 10 is not among the given options,
Correct Answer: (E) None of these ✅
⚡ Quick Trick:
If any quantity increases by x%, then:
New : Old = (100 + x) : 100
= (100 + 30) : 100
= 130 : 100
= 13 : 10
Hence, the required ratio = 13 : 10
The length of a rectangular plot is 60% more than its breadth . if the difference between the length and the breadth of that rectangle is 24 cm, what is the area of that rectangle?
Solution:
Let the breadth of the rectangle be x cm.
The length is 60% more than the breadth.
Length = x + 60% of x
= x + 0.6x
= 1.6x
Given that the difference between the length and breadth is 24 cm.
Length − Breadth = 24
1.6x − x = 24
0.6x = 24
x = 40 cm
Therefore,
Breadth = 40 cm
Length = 1.6 × 40
= 64 cm
Now, the area of the rectangle is:
Area = Length × Breadth
= 64 × 40
= 2560 sq. cm
Therefore, the area of the rectangle is 2560 sq. cm.
Correct Answer: (C) 2560 sq. cm ✅
⚡ Quick Trick:
If one quantity is 60% more than another, write them in the ratio:
Length : Breadth = 160 : 100
= 8 : 5
Difference of ratio parts = 8 − 5 = 3 parts, which equals 24 cm.
1 part = 24 ÷ 3 = 8 cm
Length = 8 × 8 = 64 cm
Breadth = 5 × 8 = 40 cm
Area = 64 × 40 = 2560 sq. cm
The length of a rectangular plot is 20 metres more than its breadth. if the cost of fencing the plot @ ₹26.50 per metres is ₹5300, what is the length of the plot in metres ?
Solution:
Let the breadth of the rectangular plot be x metres.
Since the length is 20 metres more than the breadth,
Length = x + 20
The cost of fencing the plot at ₹26.50 per metre is ₹5300.
Fencing is done along the perimeter of the plot.
Perimeter = Total Cost ÷ Rate
= 5300 ÷ 26.50
= 200 metres
Using the perimeter formula of a rectangle,
2(Length + Breadth) = 200
Length + Breadth = 100
Substituting Length = x + 20,
(x + 20) + x = 100
2x + 20 = 100
2x = 80
x = 40 metres
Therefore, the length of the plot is:
Length = 40 + 20
= 60 metres
Therefore, the length of the plot is 60 metres.
Since 60 metres is not among the given options,
Correct Answer: (E) None of these ✅
⚡ Quick Trick:
First find the perimeter using fencing cost:
Perimeter = 5300 ÷ 26.50 = 200 m
Length + Breadth = 200 ÷ 2 = 100
Given that Length is 20 m more than Breadth:
Breadth = (100 − 20) ÷ 2 = 40 m
Length = 40 + 20 = 60 m
Hence, the required length = 60 metres
Diagonals of a rhombus area 1 m and 1.5 m in lengths. The area of the rhombus is :
Solution:
Given that the lengths of the diagonals of the rhombus are 1 m and 1.5 m.
We know that the area of a rhombus is given by:
Area = ½ × d₁ × d₂
Substituting the given values,
Area = ½ × 1 × 1.5
= ½ × 1.5
= 0.75 m²
Therefore, the area of the rhombus is 0.75 m².
Correct Answer: (A) 0.75 m² ✅
⚡ Quick Trick:
Remember the direct formula for the area of a rhombus:
Area = ½ × (Product of diagonals)
= ½ × 1 × 1.5
= 0.75 m²
Hence, the required area = 0.75 m²
A rectangle has width a and length b. if the width is decreased by 20% and the length is increased by 10% , what is the area of the new rectangle in percentage compared to 'ab' ?
Solution:
Let the original width of the rectangle be a and the original length be b.
The original area of the rectangle is:
Original Area = a × b = ab
The width is decreased by 20%.
New Width = a − 20% of a
= a − 0.2a
= 0.8a
The length is increased by 10%.
New Length = b + 10% of b
= b + 0.1b
= 1.1b
Therefore, the new area of the rectangle is:
New Area = 0.8a × 1.1b
= 0.88ab
This means the new area is:
0.88ab = 88% of ab
Therefore, the new area is 88% of the original area.
Correct Answer: (B) 88% ✅
⚡ Quick Trick:
Convert percentage changes into multiplication factors:
Width factor = 80% = 0.8
Length factor = 110% = 1.1
New Area Factor = 0.8 × 1.1
= 0.88
Hence, New Area = 88% of the original area
A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for each parts folded along one set of side and the same is 38 cm when folded along the other set of side. What is the area of the paper ?
Solution:
Let the length and breadth of the rectangular paper be l cm and b cm respectively.
When the paper is folded along one set of sides, each part has dimensions l × (b/2) and perimeter 34 cm.
\[ 2\left(l + \frac{b}{2}\right) = 34 \] \[ 2l + b = 34 \quad ...(1) \]
When the paper is folded along the other set of sides, each part has dimensions (l/2) × b and perimeter 38 cm.
\[ 2\left(\frac{l}{2} + b\right) = 38 \] \[ l + 2b = 38 \quad ...(2) \]
Multiplying equation (2) by 2, we get:
\[ 2l + 4b = 76 \quad ...(3) \]
Subtracting equation (1) from equation (3):
\[ (2l + 4b) - (2l + b) = 76 - 34 \] \[ 3b = 42 \] \[ b = 14 \text{ cm} \]
Substituting b = 14 in equation (2):
\[ l + 2(14) = 38 \] \[ l = 10 \text{ cm} \]
Therefore, the area of the paper is:
\[ \text{Area} = l \times b \] \[ = 10 \times 14 \] \[ = 140 \text{ cm}^2 \]
Therefore, the area of the rectangular paper is 140 cm².
Correct Answer: (A) 140 cm² ✅
⚡ Quick Trick:
Folding along breadth gives:
\[ 2l + b = 34 \]
Folding along length gives:
\[ l + 2b = 38 \]
\[ b = 14 \text{ cm}, \quad l = 10 \text{ cm} \]
\[ \text{Area} = 10 \times 14 = 140 \text{ cm}^2 \]
The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area ?
Solution:
Let the original length and breadth of the rectangle be l and b respectively.
The original area of the rectangle is:
Original Area = l × b = lb
The length is halved while the breadth is tripled.
New Length = l/2
New Breadth = 3b
Therefore, the new area of the rectangle is:
New Area = (l/2) × 3b
= 3lb/2
= 1.5lb
This means that the new area is 150% of the original area.
Percentage Increase = 150% − 100%
= 50%
Therefore, the area increases by 50%.
Correct Answer: (B) 50% increase ✅
⚡ Quick Trick:
Convert the changes into multiplication factors:
Length Factor = 1/2
Breadth Factor = 3
Area Factor = (1/2) × 3 = 1.5
1.5 = 150%
Increase = 150% − 100% = 50%