Page 1 : Mathematics, (www.tiwariacademy.com), (Chapter-13) (Direct and Inverse Proportions), (Class - VIII), Exercise 13.1, Question 1:, Following are the car parking charges near a railway station up to:, 4 hours, 760, 8 hours, 100, 12 hours, 7140, 24 hours, 180, Check if the parking charges are in direct proportion to the parking time., EAnswer 1:, Charges per hour:, 60, = ३15, 4, 100, = 712.50, 8., C, 140, = 11.67, 12, C =, 180, = १7.50, C, =, 24, Here, the charges per hour are not same, i.e., C C, # C, ÷ C,, Therefore, the parking charges are not in direct proportion to the parking time., Question 2:, A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In, the following table, find the parts of base that need to be added., Parts of red pigment, 1, 4, 12, 20, Parts of base, 8, LAnswer 2:, Let the ratio of parts of red pigment and parts of base be, a, = 1,b = 8, = k (say), b,, Here, When, a, = 4,b, = ?, 4, = 4x8 = 32, a,, b,, k, 8, When, a, = 7.b, = ?, k = 4, b,, = 7x8=56, %3D, %3D, k, When, a, = 12,b, =?, k =, b., 12, = 12x8=96, a., %3D, 8, www.tiwariacademy.com, A Free web support in Education, 1, 1, 7-

Page 2 : Mathematics, (www.tiwariacademy.com), (Chapter-13) (Direct and Inverse Proportions), (Class - VIII), When, a, = 20, b, = ?, as, b,, k, 20, = 20x8 160, as, k =, b,, %3D, 8., Parts of red pigment, 1, 4, 7, 12, 20, Parts of base, 8., 32, 56, 96, 160, Question 3:, In Question 2 above, if 1 part of a red pigment requires 75 ml of base, how much red, pigment should we mix with 1800 mL of base?, LAnswer 3:, Let the parts of red pigment mix with 1800 mL base be x., Parts of red pigment, 1, Parts of base, 75, 1800, Since it is in direct proportion., Ix1800, » 75x.r=1x1800, 24 parts, → x=, 75 1800, 75, Hence, with base 1800 ml, 24 parts red pigment should be mixed., Question 4:, A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill, in five hours?, LAnswer 4:, Let the number of bottles filled in five hours be x., Hours, 1, Bottles, 75, 1800, Here ratio of hours and bottles are in direct proportion., 5x840, > X=, 6., 6., > 6xx =5x840, 700 bottles, 840, Hence, machine will fill 700 bottles in five hours., Question 5:, A photograph of a bacteria enlarged 50,000 times attains a, length of 5 cm as shown in the diagram. What is the actual, length of the bacteria? If the photograph is enlarged 20,000, times only, what would be its enlarged length?, LAnswer 5:, Let enlarged length of bacteria be x., 5, Actual length of bacteria =, cm = 10 cm, 50000 10000, Length, 5, Enlarged length, 50,000, 20,000, Here length and enlarged length of bacteria are in direct proportion., www.tiwariacademy.com, A Free web support in Education, 2, 2

Page 3 : Mathematics, (www.tiwariacademy.com), (Chapter- 13) (Direct and Inverse Propertions), (Class- VIII), 5, 5x 20000, = xx 50000 = 5x 20000 = x =, = 2 cm, 50000, 20000, 50000, Hence, the enlarged length of bacteria is 2 cm., Question 6:, In a model of a ship, the mast is 9 cm high, while the, mast of the actual ship is 12 m high. If the length if the, ship is 28 m, how long is the model ship?, LAnswer 6:, Let the length of model ship be x., Length of actual ship (in m), Length of model ship (in cm), Here length of mast and actual length of ship are in direct proportion., 12, 28, 9., 12 28, 28x9, > xx12 28x9, → x=, - 21 ст, 9., Hence, the length of the model ship is 21 cm., 12, Question 7:, Suppose 2 kg of sugar contains 9 x 106 crystals. How many sugar crystals are there in (i), 5 kg of sugar? (ii) 1.2 kg of sugar?, LAnswer 7:, Let sugar crystals be x., Weight of sugar (in kg), No. of crystals, Here weight of sugar and number of crystals are in direct proportion., (i), 2, 9x10", 5x9x10°, 5, 9x10 x, Hence, the number of sugar crystals is 2.25x10., > xx 2 = 5x9x10, = 22.5x10 = 2.25 x 10', (ii), Let sugar crystals be, Weight of sugar (in kg), 2, 1.2, No. of crystals, 9x 10, Here weight of sugar and number of crystals are in direct proportion., 2, 1.2, = xx 2 = 1.2 x9x10° x =, 1.2x9x10, = 0.6x9x10° = 5.4x10°, 9x10, Hence, the number of sugar crystals is 5.4x 10"., Question 8:, Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for, 72 km. What would be her distance covered in the map?, LAnswer 8:, Let distance covered in the map be x., Actual distance (in km), 18, 72, www.tiwariacademy.com, A Free web support in Education, 3, 3

Page 4 : Mathematics, (www.tiwariacademy.com), (Chapter-13) (Direct and Inverse Proportions), (Class - VIII), Distance covered in map (in cm), Here actual distance and distance covered in the map are in direct proportion., 1, 18 72, = xx18 = 72x1, 72x1, = 4 cm, 18, → x=, Hence, the distance covered in the map is 4 cm., Question 9:, A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time (i), the length of the shadow cast by another pole 10 m 50 cm high (ii) the height of a pole, which casts a shadow 5 m long., E Answer 9:, Here height of the pole and length of the shadow are in direct proportion., And 1m = 100 cm, 5 m 60 cm = 5 x 100 + 60 = 560 cm, 3 m 20 cm = 3 x 100 + 20 = 320 cm, 10 m 50 cm = 10 x 100 + 50 = 1050 cm, 5 m = 5 x 100 = 500 cm, Let the length of the shadow of another pole be x., (i)., Height of pole (in cm), Length of shadow (in cm), 560, 1050, 320, 560, 1050, 1050x320, = xx 560 = 1050x320 x=, = 600 cm 6 m, 320, 560, Hence, the length of the shadow of another pole is 6 m., Let the height of the pole be x., (ii)., Height of pole (in cm), 560, Length of shadow, (in cm), 320, 500, 560, 560x500, → xx 320 = 560x500 x=, 875 cm = 8 m 75 cm, 320 500, 320, Hence, the height of the pole is 8 m 75 cm., Question 10:, A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it, travel in 5 hours?, LAnswer 10:, Let distance covered in 5 hours be x km., 1 hour = 60 minutes, 5 hours = 5 x 60 = 300 minutes, Distance (in km), Time (in minutes), Here distance covered and time in direct proportion., 14, 25, 300, 14, 14x300, → xx 25 = 14x300 x=, 25, = 168 km, 25 300, Hence, the distance covered in 5 hours is 168 km., www.tiwariacademy.com, A Free web support in Education, 4, 4

Page 5 : Mathematics, (www.tiwariacademy.com), Chapter - 13) (Direct and Inverse Proportions), (Class - VIII), Exercise 13.2, Question 1:, Which of the following are in inverse proportion:, (i), The number of workers on a job and the time to complete, the job., The time taken for a journey and the distance travelled in, (ii), a uniform speed., (iii) Area of cultivated land and the crop harvested., The time taken for a fixed journey and the speed of the, vehicle., (iv), The population of a country and the area of land per person., (v), E Answer 1:, (i), The number of workers and the time to complete the job is in inverse, proportion because less workers will take more time to complete a work, and more workers will take less time to complete the same work., Time and distance covered in direct proportion., It is a direct proportion because more are of cultivated land will yield more, (ii), (iii), crops., (iv), Time and speed are inverse proportion because if time is less, speed is, more., It is a inverse proportion. If the population of a country increases, the area, of land per person decreases., (v), Question 2:, In a Television game show, the prize money of 1,00,000 is to be divided equally amongst, the winners. Complete the following table and find whether the prize money given to an, individual winner is directly or inversely proportional to the number of winners:, No. of winners, 1, 2, 4, 8, 10, 20, 50,000, Prize for each winner (in 7) 1,00,000, LAnswer 2:, Here number of winners and prize money are in inverse proportion because, winners are increasing, prize money is decreasing., 100000, When the number of winners are 4, each winner will get =, = 725,000, 100000, When the number of winners are 5, each winner will get, = 20,000, 100000, When the number of winners are 8, each winner will get =, 8, = 12,500, 100000, When the number of winners are 10, each winner will get =, 10, = 10,000, 100000, When the number of winners are 20, each winner will get =, = १5,000, 20, www.tiwariacademy.com, A Free web support in Education, 1, 5