QUANTITATIVE APTITUDE

Transcription

1 SBI Probationery Officers QUANTITATIVE APTITUDE Mensuration (Plane Figures) Mensuration is one of the branches of mathematics. This means measurement. It is being done in our life in many situations. Here, we cover three areas, Perimeter, Area and Volume. To find these things we have to remember the formulae of plane figures and solid figures. Try to understand the concept behind reaching the formula. Triangle: If a, b and c are the lengths of the sides of a triangle, Area = s(s a)(s b)(s c) a + b + c Where s = 3 Area of equilateral triangle = (side) 4 b Area of an isosceles triangle = 4a b 4 1 Area of a right angled triangle = base height Square: Area = side Perimeter = 4 side Rectangle: Area = length breadth Perimeter = (length + breadth) Rhombus: 1 Area = d 1 d Perimeter = 4(d 1 + d ) d 1, d = diagonals Parallelogram: Area = b h b = base, h = perpendicular height Trapezium: 1 Area = h (a + b) h = perpendicular height a, b = parallel sides R

2 Circle: Area = πr r = radius Circumference = πr 0 Area of sector = πr Length of the arc = πr 360 Semi Circle: πr Area = 36 Circumference = radius Units of Measuring Length 10 millimeter = 1 centimeter 10 centimeter = 1 decimeter 10 decimeter = 1 meter 10 meter = 1decameter 10 decameter = 1 hectometer 10 hectometer = 1 kilometer EXERCISE 1. The area of a rectangular plate is sq.cm. If the length of the plate is 19.5 cm, find the perimeter of the plate. 1) 65 cm ) 5 cm 3) 6 cm 4) 68.5 cm 5) None of these. The breadth of a rectangular plot is 5% of its length. If the perimeter of the plot be 1050 m, what is its area? 1) 1500 ) ) ) ) None of these 3. How many metres of carpet 5 cm wide will be required to cover the floor of a room which is 0 metres long and 1 metres broad? 1) 10 m ) 90 m 3) 30 m 4) 30 m 5) None of these 4. How many tiles of 0 cm length and 10 cm width are required to pave the floor of a room 8 m long and 5 m wide? 1) 100 ) ) 500 4) 000 5) None of these 5. The circumference of two circles is 88 metre and 13 metre respectively. What is the difference between the area of the larger circle and the smaller circle? 1) 440 sq.m. ) 510 sq.m. 3) 0 sq.m. 4) 5 sq.m. 5) None

3 6. A rectangular hall 1 metres long and 10 m broad is surrounded by a verandah metres wide. Find the area of the verandah. 1) 104 sq.m. ) 9 sq.m. 3) 116 sq.m. 4) 48 sq.m. 5) None of these. In measuring the sides of a rectangle, one side is taken 10% in excess, and the other 5% in deficit. What is the change in its area as a percentage? 1) 1.5% ) 4.5% 3).5% 4) 5% 5) None of these 8. A square field has an area of 5065 sq.m. Find the cost of two line fencing around it at Rs.15 per metre. 1) Rs.1,500 ) Rs.1,500 3) Rs.13,500 4) Rs.16,50 5) None of these 9. Cost of fencing a circular plot at the rate of Rs.1 per metre is Rs.,640. What will be the cost of carpeting the floor of the plot at the rate of Rs.5 per square metre? 1) Rs.1,5,50 ) Rs.96,50 3) Rs.8,50 4) Rs.5,50 5) None of these 10. A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 6 cm. What will be the area of the circle? 1) 88 cm ) 150 cm 3) 154 cm 4) 18 cm 5) None of these 11. A circular garden has a m wide road around the border. Find the cost of leveling the road at Rs.150 per square meter if the radius of the inner circle is 1 m? 1) Rs.3,49,000 ) Rs.53,900 3) Rs.1,61,00 4) Rs.1,45,600 5) None of these ml paint is required to paint a circular plate of 5 cm. How much paint is required to paint a similar plate of radius 5 cm? 1) 105 ml ) 0 ml 3) 315 ml 4) 10 ml 5) None of these 13. The length and breadth of a rectangle increased by 0% and 10% respectively. How much percent will its area be increased? 1) 5% ) 30% 3) 40% 4) 3% 5) None 14. A horse is tied with a 14 m long rope. How much ground will it be able to graze? 1) 15 sq.m. ) 5 sq.m. 3) 65 sq.m. 4) 65 sq.m. 5) None 15. A rectangular field of 60 metre long and 40 metre wide is to be surrounded by a road 5 metre wide. If the cost of making one square meter road is Rs.500, what would be the cost of the entire road? 1) Rs.6,5,000 ) Rs.5,55,000 3) Rs.5,50,000 4) Rs.5,6,500 5) None of these KEY 1-4; -; 3-3; 4-4; 5-3; 6-1; -; 8-5; 9-; 10-5; 11-3; 1-3; 13-4; 14-5; 15-3.

4 EXPLANATIONS Width of the plate = = 14.5 cm 19.5 Perimeter = (length + width) ( ) = 68.5 cm. Let the length of the plot be x m 5 3x Breadth = x = x 1050 = ( ) x + 4 x = Area of the plot = = 6500 m 3. Area of carpet = Width of carpet = 5 cm = m Length of carpet = = 0 1 = 30 metres 3 4. Area of the floor of the room = ( ) cm Area of the Tile = (0 10) cm Number of Tiles required = 0 10 = Let the radius of larger circle be R and smaller circle be r πr = 13 R = 13 R = 1 πr = 88 r = 88 r = 14 Difference in the areas = πr πr = π(r r ) (1 14 ) (1 + 14) (1 14) 35 = 0 sq.metres 6. Area of the verandah = outer rectangle inner rectangle ( ) = 104 sq.m.

5 . Let the length be 10 and breadth also be 10 Area = = 100 New length (10% excess) = 11 New breadth (5% deficit) = 9.5 New area = = Change in area = = Percentage change = 100 = 4.5% Side of the square field = 5065 = 5 m Length of the wire required = 4 5 = 900 = 1800 m Total cost = Rs = Rs., Circumference of the circular plot = 1 = 0 m πr = 0 r = 0 r = 35 m Area of the plot = πr = = 3850 sq.m. Cost of carpeting = 3850 Rs.5 = Rs.96, Perimeter of rectangle = (18 + 6) = 88 cm Circumference of circle πr = 88 r = 88 r = 14 cm Area of circle = πr = = 616 cm 11. Radius of outer circle = 1 + = 8 m Road area = Area of outside circle Area of inside circle Road area = π(8) π(1) = 108 sq.m. Cost = 108 Rs.150 = Rs.1,61,00 1. Ratio of radius of two circular plates = 5 : 5 = 1 : 3 Ratio of areas of two plates = π(1) : π(3) = 1 : 9 i.e., area of second plate is 9 times the area of the first plate Paint required = 9 35 = 315 ml

6 13. Let the length be 10 and breadth also be 10 Area = = 100 New length (0% excess) = 1 New breadth (10% excess) = 11 New area = 1 11 = 13 Change in area = = 3 Percentage increase = 3% 14. Length of the rope will be the radius of the circle = 14 m Area of the circle = πr = = 616 sq.m. Area of the ground that can be grazed = 616 sq.m 15. Area of the road = Area of outside rectangle Area of inside rectangle = = = 1100 m The cost of making 1100 m = = Rs.5,50,000 Writer: Dr. G.S. Giridhar