General Questions
Practice and master this topic with our carefully crafted questions.
Radhika runs along the boundary of a rectangular park at the rate of 12 km/hr and completes one full round in 15 minutes. If the length of the park is 4 times its breadth, the area of the park is ?
Solution:
Radhika runs at the rate of 12 km/hr and completes one round of the park in 15 minutes.
Distance covered in one round = Perimeter of the rectangular park.
Time = 15 minutes = 15/60 hour = 1/4 hour
Perimeter = Speed × Time
= 12 × 1/4 km
= 3 km = 3000 m
Let the breadth of the park be x m.
Since the length is 4 times the breadth,
Length = 4x
The perimeter of the rectangle is:
2(Length + Breadth) = 3000
2(4x + x) = 3000
10x = 3000
x = 300 m
Therefore,
Breadth = 300 m
Length = 4 × 300 = 1200 m
Now, the area of the park is:
Area = Length × Breadth
= 1200 × 300
= 360000 m²
Therefore, the area of the park is 360000 m².
Correct Answer: (A) 360000 m² ✅
⚡ Quick Trick:
First find the perimeter using:
Perimeter = Speed × Time
= 12 × 1/4 km = 3 km = 3000 m
Length : Breadth = 4 : 1
Total ratio parts = 4 + 1 = 5
2 × 5 = 10 parts = 3000 m
1 part = 300 m
Area = 1200 × 300 = 360000 m²
The ratio between the length and the breadth of a rectangular park is 3 : 2. if a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is :
Solution:
The ratio between the length and breadth of the rectangular park is 3 : 2.
Let the length and breadth be 3x m and 2x m respectively.
A man cycles at the speed of 12 km/hr and completes one round in 8 minutes.
Time = 8/60 hr = 2/15 hr
Perimeter = Speed × Time
= 12 × 2/15 km
= 1.6 km = 1600 m
Since one round of the park is its perimeter,
2(Length + Breadth) = 1600
2(3x + 2x) = 1600
10x = 1600
x = 160
Therefore,
Length = 3 × 160 = 480 m
Breadth = 2 × 160 = 320 m
Area of the park is:
Area = Length × Breadth
= 480 × 320
= 153600 sq. m
Therefore, the area of the park is 153600 sq. m.
Correct Answer: (B) 153600
⚡ Quick Trick:
Length : Breadth = 3 : 2, so let them be 3x and 2x.
Perimeter = 12 × (8/60) km
= 1.6 km = 1600 m
2(3x + 2x) = 1600
x = 160
Area = 480 × 320 = 153600 sq. m
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. if the area of the field is 680 sq. feet, how many feet of fencing will be required ?
Correct Answer: D. 88 ✅
- A. 34 ❌
- B. 40 ❌
- C. 68 ❌
- D. 88 ✅ — Correct.
Explanation:
The area of the rectangular field is 680 sq. ft. and one side is 20 ft.
Using the formula:
Area = Length × Breadth
680 = 20 × Breadth
Breadth = 680 ÷ 20
Breadth = 34 ft
So, the dimensions of the field are 20 ft × 34 ft.
Since one side of 20 ft is left uncovered, fencing is required for the other three sides:
34 + 20 + 34 = 88 ft
Therefore, the required fencing is 88 feet.
Exam Fact:
For a rectangular field fenced on three sides, first find the missing side using Area = Length × Breadth, then add only the three sides that are fenced.
Therefore, the correct answer is D. 88 ✅.
The length of a rectangular hall is 5 m more than its breadth. The area of the hall is 750m.sq. The length of the hall is :
Correct Answer: D. 30 m ✅
- A. 15 m ❌
- B. 22.5 m ❌
- C. 25 m ❌ — This is the breadth, not the length.
- D. 30 m ✅ — Correct.
Explanation:
Let the breadth of the hall be x m.
The length is 5 m more than the breadth:
Length = x + 5
We know:
Area = Length × Breadth
x(x + 5) = 750
x² + 5x − 750 = 0
Factorising:
(x + 30)(x − 25) = 0
Therefore:
Breadth = 25 m
Hence:
Length = 25 + 5
= 30 m
Quick Check:
30 × 25 = 750 m² ✔️
30 − 25 = 5 m ✔️
Exam Fact:
When the length is a fixed amount more than the breadth, take the breadth as x, form the area equation, and then add the given difference to find the length.
Therefore, the correct answer is D. 30 m ✅.
A took 15 second to cross a rectangular field diagonally walking at the rate of 52 m / min and B took the same time to cross the same field along its sides walking at the rate of 68 m / min. The area of the field is :
Correct Answer: D. 60 m² ✅
- A. 30 m² ❌
- B. 40 m² ❌
- C. 50 m² ❌
- D. 60 m² ✅ — Correct.
Explanation:
Both A and B take 15 seconds to cross the field.
Convert 15 seconds into minutes:
15 seconds = 15/60 = 1/4 minute
Step 1: Find the diagonal
Diagonal = Speed × Time
= 52 × 1/4
= 13 m
So, the diagonal of the rectangular field is 13 m.
Step 2: Find the total length along the sides
Distance covered by B = 68 × 1/4
= 17 m
Since B crosses the field along its two sides:
Length + Breadth = 17 m
We also know from Pythagoras:
Length² + Breadth² = Diagonal²
Length² + Breadth² = 13²
= 169
Now use:
(Length + Breadth)² = Length² + Breadth² + 2(Length × Breadth)
17² = 169 + 2(Length × Breadth)
289 = 169 + 2(Length × Breadth)
120 = 2(Length × Breadth)
Length × Breadth = 60
Therefore:
Area = Length × Breadth = 60 m²
Exam Fact:
If the sum of two sides and the diagonal of a rectangle are known, use:
(L + B)² = L² + B² + 2LB
Therefore, the correct answer is D. 60 m² ✅.
A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is :
Correct Answer: D. 28% ✅
- A. 10% ❌
- B. 10.08% ❌
- C. 20% ❌
- D. 28% ✅ — Correct.
Explanation:
Suppose the original length of the towel is 100 cm and its breadth is 100 cm.
After bleaching:
New length = 100 − 20% of 100
= 80 cm
New breadth = 100 − 10% of 100
= 90 cm
Original area:
100 × 100 = 10,000 cm²
New area:
80 × 90 = 7,200 cm²
Decrease in area:
10,000 − 7,200 = 2,800 cm²
Percentage decrease:
(2,800 ÷ 10,000) × 100
= 28%
Therefore, the percentage decrease in area is 28%.
Exam Fact:
When two dimensions decrease by different percentages, the percentage decrease in area is:
x + y − (xy/100)
Here:
20 + 10 − (20 × 10)/100
= 30 − 2
= 28%
Therefore, the correct answer is D. 28% ✅.
The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is :
Correct Answer: B. 44% ✅
- A. 40% ❌
- B. 44% ✅ — Correct.
- C. 42% ❌
- D. 46% ❌
Explanation:
Suppose the original length and breadth of the rectangle are 100 m each.
Each side is increased by 20%.
New length = 100 + 20% of 100 = 120 m
New breadth = 100 + 20% of 100 = 120 m
Original area:
100 × 100 = 10,000 m²
New area:
120 × 120 = 14,400 m²
Increase in area:
14,400 − 10,000 = 4,400 m²
Percentage increase:
(4,400 ÷ 10,000) × 100
= 44%
Quick Trick:
When both sides increase by the same percentage:
Increase in area = 2x + (x²/100)
= 2(20) + (20²/100)
= 40 + 4
= 44%
Exam Fact:
A 20% increase in each side does not mean a 40% increase in area because the additional 4% comes from the increase in both dimensions together.
Therefore, the correct answer is B. 44% ✅.
What will be the cost of gardening 1 metre broad boundary around a rectangular plot having perimeter of 340 metres at the rate of Rs.10 per sqare metres ?
Correct Answer: C. ₹3440 ✅
- A. ₹1700 ❌
- B. ₹3400 ❌
- C. ₹3440 ✅ — Correct.
- D. Cannot be determined ❌
- E. None of these ❌
Explanation:
The rectangular plot has a perimeter of 340 m.
A 1 m broad boundary is made around the plot. Since the boundary is around the outside, the area of the boundary is:
Area of boundary = Perimeter × Width + 4 × Width²
Here:
Perimeter = 340 m
Width = 1 m
Area of boundary = 340 × 1 + 4 × 1²
= 340 + 4
= 344 m²
Cost of gardening is ₹10 per m².
Total cost = 344 × 10
= ₹3440
Exam Fact:
For a 1 m wide boundary outside a rectangular plot, the boundary area is not simply perimeter × 1 because the four corner squares also contribute area.
Therefore, the correct answer is C. ₹3440 ✅.
The ratio between the perimeter and the breadth of a rectangle is 5 : 1. if the area of the rectangle is 216 sq. cm, what is the length of the rectangle ?
Correct Answer: B. 18 cm ✅
- A. 16 cm ❌
- B. 18 cm ✅ — Correct.
- C. 24 cm ❌
- D. Data inadequate ❌
- E. None of these ❌
Explanation:
Let the length of the rectangle be L and breadth be B.
Given:
Perimeter : Breadth = 5 : 1
The perimeter of a rectangle is:
Perimeter = 2(L + B)
Therefore:
2(L + B) / B = 5
2L + 2B = 5B
2L = 3B
L = 3B/2
We are given that the area is 216 cm².
Area = Length × Breadth
(3B/2) × B = 216
3B² = 432
B² = 144
B = 12 cm
Therefore:
L = 3/2 × 12
= 18 cm
Quick Check:
Perimeter = 2(18 + 12) = 60 cm
60 : 12 = 5 : 1 ✔️
Area = 18 × 12 = 216 cm² ✔️
Exam Fact:
For a rectangle, use Perimeter = 2(L + B) and Area = L × B. When a ratio involving perimeter and breadth is given, first form the relationship between L and B.
Therefore, the correct answer is B. 18 cm ✅.
The length of a rectangle is decreased by r%, and the breadth is increased by (r+5)%.Find r, if the area of the rectangle is unaltered.
Correct Answer: E. 20 ✅
- A. 5 ❌
- B. 8 ❌
- C. 10 ❌
- D. 15 ❌
- E. 20 ✅ — Correct.
Explanation:
Let the original length = L and breadth = B.
New length = L(1 − r/100)
New breadth = B(1 + (r+5)/100)
Since area remains unchanged:
(1 − r/100)(1 + (r+5)/100) = 1
For r = 20:
(1 − 20/100)(1 + 25/100)
= 0.8 × 1.25
= 1
So the area remains unchanged.
Exam Fact:
When dimensions change by percentages and area remains unchanged, multiply the new percentage factors and equate the result to 1.
Therefore, the correct answer is E. 20 ✅.