(IGP) IAS Pre Paper - 2: GS - Basic Numeracy - Area of Plane Figures (MCQ -15)

1. A rectangular carpet has an area of 120 sq.metres and a perimeter of 46 metres. The length of its diagonal is:
(a) 15 m
(b) 19 m
(c) 17 m
(d) 22 m

2. A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52m/min and B took the same time to cross the same field along its sideswalking at the rate of 68m/min. The area of the field is:
(a) 52 m²
(b) 40 m²
(c) 61 m²
(d) 60 m²

3. A rectangular carpet has an area of 60 sq. m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is:
(a) 8 m
(b) 12 m
(c) 15 m
(d) 14.5 m

4. The ratio between the length and the breadth of a rectangular field is 3 : 2. If only the length is increased by 5 metres, the new area of the field will be 2600 sq. metres. What is the breadth of the rectangular field?
(a) 40metres
(b) 80metres
(c) 66metres
(d) cannot be determined

5. The length of a blackboard is 8 cm more than its breadth. If the length is increased by 7 cm and breadth is decreased by 4 cm, the area remains the same. The length and breadth of the blackboard (in cm) will be:
(a) 28, 20
(b) 36, 26
(c) 40, 32
(d) 58, 48

6. 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:
(a) 11%
(b) 12%
(c) 20%
(d) 28%

7. If the area of a rectangular plot increases by 30% while its breadth remains same, what will be the ratio of the areas of new and old figures?
(a) 4 : 3
(b) 5 : 1
(c) 4 : 7
(d) 11 : 13

8. 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:
(a) 40
(b) 70
(c) 64
(d) 75

9. A room is 15 feet long and 12 feet broad. A mat has to be placed on the floor of this room leaving 1½ feet space from the walls. What will be the cost of the mat at the rate of Rs. 3.50 per square feet?
(a) Rs. 378
(b) Rs. 638
(c) Rs. 496
(d) Rs. 635

10. What will be the cost of gardening 1metre broad boundary around a rectangular plot having perimeter of 340 metres at the rate of Rs. 10 per square metre?
(a) Rs. 1900
(b) Rs. 3600
(c) Rs. 3440
(d) cannot be determined

11. 2 metres broad 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.
(a) Rs. 3600
(b) Rs. 5000
(c) Rs. 4800
(d) data inadequate

12. Within a rectangular garden 10 m wide and 20 mlong,wewish to pave awalk around the borders of uniform width so as to leave an area of 96 m2 for flowers. How wide should the walk be?
(a) 3.2 m
(b) 2 m
(c) 2.7 m
(d) 3.5 m

13. A rectangular lawn 55 m by 35 m has two roads each 4 m wide running in the middle of it, one parallel to length and the other parallel to breadth. The cost of gravelling the roads at 75 paise per sq. metre is:
(a) Rs. 257.50
(b) Rs. 258
(c) Rs. 262.50
(d) Rs. 275

14. A rectangular park 60m 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?
(a) 4.50 m
(b) 4 m
(c) 6.50 m
(d) None of these

15. A housing society has been allotted a square piece of landmeasuring 2550.25 sq.m.What is the side of the plot?
(a) 52.65 m
(b) 50.5 m
(c) 50.65 m
(d) 50.15 m

16. The cost of cultivating a square field at the rate of Rs. 135 per hectare is Rs. 1215. The cost of putting a fence around it at the rate of 75 paise permetre would be
(a) Rs. 480
(b) Rs. 815
(c) Rs. 900
(d) Rs. 1900

17. The length and breadth of a rectangular park are 15 m and 8 m respectively. The perimeter of the park is
(a) 40 m
(b) 42 m
(c) 44 m
(d) 46 m

18. One side of a rectangular lawn is 12 m and the diagonal is 13 m. Find the area of the field
(a) 30 m²
(b) 45 m²
(c) 60 m²
(d) 90 m²

19. The length of a rectangle is 1 cm more than its breadth. The diagonal is 29 cm. Find the area of the rectangle
(a) 481 cm²
(b) 841 cm²
(c) 420 cm²
(d) 870 cm²

20. A rectangular grassy lawn is 18m × 12 m. It has a gravel path 1.5 m wide all around it on the outside. What is the area of the path?
(a) 99 m²
(b) 100 m²
(c) 101 m²
(d) 102 m²

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