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- Question
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?
Options- A. 34
- B. 40
- C. 68
- D. 88
- Correct Answer
- 88
ExplanationWe have: l = 20 ft and lb = 680 sq. ft.So, b = 34 ft.
∴ Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft.
Area problems
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- 1. The diagonal of the floor of a rectangular closet is 7½ feet. The shorter side of the closet is 4½ feet. What is the area of the closet in square feet?
Options- A.
5 1 4 - B.
13 1 2 - C. 27
- D. 37 Discuss
Correct Answer: 27
Explanation:
Other side = ❨ 15 ❩ 2 - ❨ 9 ❩ 2 2 2 ft = 225 - 81 4 4 ft = 144 4 ft = 6 ft. ∴ Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.
- 2. The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?
Options- A. 40
- B. 50
- C. 120
- D. Data inadequate
- E. None of these Discuss
Correct Answer: None of these
Explanation:
Let breadth = x metres.Then, length = (x + 20) metres.
Perimeter = ❨ 5300 ❩ m = 200 m. 26.50 ∴ 2[(x + 20) + x] = 200
⟹ 2x + 20 = 100
⟹ 2x = 80
⟹ x = 40.
Hence, length = x + 20 = 60 m.
- 3. 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:
Options- A. 10%
- B. 10.08%
- C. 20%
- D. 28% Discuss
Correct Answer: 28%
Explanation:
Let original length = x and original breadth = y.Decrease in area = xy - ❨ 80 x x 90 y ❩ 100 100 = ❨ xy - 18 xy ❩ 25 = 7 xy. 25 ∴ Decrease % = ❨ 7 xy x 1 x 100 ❩% = 28%. 25 xy - 4. The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?
Options- A. 25% increase
- B. 50% increase
- C. 50% decrease
- D. 75% decrease Discuss
Correct Answer: 50% increase
Explanation:
Let original length = x and original breadth = y.Original area = xy.
New length = x . 2 New breadth = 3y.
New area = ❨ x x 3y ❩ = 3 xy. 2 2 ∴ Increase % = ❨ 1 xy x 1 x 100 ❩% = 50%. 2 xy - 5. How many times in a day, are the hands of a clock in straight line but opposite in direction?
Options- A. 20
- B. 22
- C. 24
- D. 48 Discuss
Correct Answer: 22
Explanation:
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).So, in a day, the hands point in the opposite directions 22 times.
- 6. An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
Options- A. 2%
- B. 2.02%
- C. 4%
- D. 4.04% Discuss
Correct Answer: 4.04%
Explanation:
100 cm is read as 102 cm.∴ A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
∴ Percentage error = ❨ 404 x 100 ❩% = 4.04% 100 x 100 - 7. A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?
Options- A. 20
- B. 24
- C. 30
- D. 33 Discuss
Correct Answer: 30
Explanation:
Let the side of the square(ABCD) be x metres.Then, AB + BC = 2x metres.
AC = √2x = (1.41x) m.
Saving on 2x metres = (0.59x) m.
Saving % = ❨ 0.59x x 100 ❩% = 30% (approx.) 2x - 8. 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:
Options- A. 15360
- B. 153600
- C. 30720
- D. 307200 Discuss
Correct Answer: 153600
Explanation:
Perimeter = Distance covered in 8 min. = ❨ 12000 x 8 ❩m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
∴ Length = 480 m and Breadth = 320 m.
∴ Area = (480 x 320) m2 = 153600 m2.
- 9. The diagonal of a rectangle is √41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:
Options- A. 9 cm
- B. 18 cm
- C. 20 cm
- D. 41 cm Discuss
Correct Answer: 18 cm
Explanation:
√l2 + b2 = √41.Also, lb = 20.
(l + b)2 = (l2 + b2) + 2lb = 41 + 40 = 81
⟹ (l + b) = 9.
∴ Perimeter = 2(l + b) = 18 cm.
- 10. 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?
Options- A. 2.91 m
- B. 3 m
- C. 5.82 m
- D. None of these Discuss
Correct Answer: 3 m
Explanation:
Area of the park = (60 x 40) m2 = 2400 m2.Area of the lawn = 2109 m2.
∴ Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
⟹ x2 - 100x + 291 = 0
⟹ (x - 97)(x - 3) = 0
⟹ x = 3.
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