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#### List of direct and inverse proportions Questions

Question No | Questions | Class |
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1 | The cube root of ( x ) varies inversely as the square of y. If ( x=8 ) when ( y=3 ), then find ( mathbf{x} ) when ( boldsymbol{y}=mathbf{1} frac{mathbf{1}}{mathbf{2}} ) | 8 |

2 | ( x ) ( begin{array}{ccccc}mathbf{2} & mathbf{3} & mathbf{5} & mathbf{6} & mathbf{1 0} \ 15 & 10 & b & 5 & 3end{array} ) ( y ) Identify the inverse proportional quantities. ( mathbf{A} cdot 4 ) B. 5 ( mathbf{c} cdot mathbf{6} ) D. 10 | 8 |

3 | 57. If x: y = 3:4, then 4x + 5y: 5x – 2y = (1) 7: 32 (2) 32:7 (3) 4:3 (4) 5 : 2 | 8 |

4 | If ( a ) is inversely proportional to ( b ) and ( b ) is inversely proportional to ( c ) then what is proportionality between ( a ) and ( c ? ) A. Direct B. Inverse c. No proportionality D. can’t be determinal | 8 |

5 | Which of the following is an example of indirect proportion? A. Number of mangoes in a bag and weight of the bag. B. Earning and hours worked. c. More the speed, lesser the time taken D. None of these. | 8 |

6 | A car travels ( 40 mathrm{km} mathrm{s} ) in 30 mins. If the speed of bus remains same, how far can it travel in 3 hrs? A. ( 120 mathrm{km} ) B. ( 80 mathrm{km} ) ( c .240 k m ) D. None of these | 8 |

7 | 59. If x varies inversely as (y – 1) and is equal to 24 when y = 10, then the value of x when y=5 is (1) 99 (2) 12 (3) 24 (4) 100 | 8 |

8 | 55 cows can graze a field in 16 days. How many cows will graze the same field in 10 days? | 8 |

9 | Mark the correct alternative of the following. If six men can do a piece of work in 6 | 8 |

10 | Find the value of ( x ) if ( a ) and ( b ) are in direct proportion ( begin{array}{ccccc}a & 2 & 3 & 4 & 5 \ b & 14 & 21 & x & 35end{array} ) A . 16 в. 25 c. 27 D. 28 | 8 |

11 | Share of ( A, B ) and ( C ) respectively, are if Rs. ( mathbf{5 4 6 0} ) is divided in ( frac{1}{2}: frac{1}{3}: frac{1}{4} ) A . Rs. 1680 , Rs. 2520 , Rs. 1260 B. Rs. 2520, Rs. 1680, Rs. 1260 c. Rs. ( 1260, ) Rs. ( 2100, ) Rs. 2520 D. Rs. ( 2520, ) Rs. ( 1260, ) Rs. 1680 | 8 |

12 | 1200 men can finish a stock of food in 35 days. How many more men should join them so that the same stock may last for 25 days? | 8 |

13 | If y varies inversely with the fourth root of ( x, ) and ( y=4 ) when ( x=frac{1}{16}, ) then what is the value of ( y ) when ( x=frac{1}{81} ) | 8 |

14 | If ( x ) and ( y ) vary inversely as each other, and ( x=10 ) when ( y=6 . ) Find ( y ) when ( boldsymbol{x}=mathbf{1 5} ) A . 2 B. 4 c. 8 D. | 8 |

15 | 52. The prices of a school bag and a shoe are in the ratio 7:5. The price of a school bag is 200 more than the price of a shoe. Then the price of a shoe is (1) 200 (2) 700 (3) 500 (4) 1,200 | 8 |

16 | Suppose 2 kg of sugar contains 9106 crystals. How many sugar crystals are there in (i) 5 kg of sugar? (ii) ( 1.2 mathrm{kg} ) of sugar? | 8 |

17 | If 30 men can reap a field in 14 days, in how many days will 20 men reap it? | 8 |

18 | Which of the following are in inverse proportion? (i) The number of workers on a job and the time to complete the job. (ii) The time taken for a journey and the distance travelled in a uniform speed. (iii) Area of cultivated land and the crop harvested. (iv) The time taken for a fixed journey and the speed of the vehicle. (v) The population of a country and the area of land per person. | 8 |

19 | Which is an example of inverse proportion? A. More amount of sweets, more total cost B. More length of cloth, more cost C. More expenditure, less saving D. More height of object, more length of its shadow | 8 |

20 | A farmer has enough food to feed 28 animals in his cattle for 9 days. How long would the food last if there were 8 more animals in his cattle ? A . 5 B. 7 c. 10 D. None of these | 8 |

21 | The cost of 3 digital cameras and 5 cell phones is Rs. ( 35,290 . ) What is the cost of 9 digital cameras and 15 cell phones? A . Rs. 1,68,450 B. Rs. 1,79,220 c. Rs. 1,05,870 D. None of these | 8 |

22 | Four angles of a quadrilateral are in the ratio ( 3: 5: 7: 9 . ) The greatest angle is A . ( 125^{circ} ) B . ( 75^{circ} ) ( mathbf{c} cdot 135^{circ} ) D. ( 120^{circ} ) | 8 |

23 | 58. In a mixture of 25 litres, the ra- tio of acid to water is 4: 1. An- other 3 litres of water is added to the mixture. The ratio of acid to water in the new mixture is (1) 5:2 (2) 2:5 (3) 3:5 (4) 5:3 | 8 |

24 | A 5 m ( 60 mathrm{cm} ) high vertical pole casts a shadow ( 3 m 20 mathrm{cm} ) long. Find at the same time (i) the length of the shadow cast by another pole 10 m ( 50 mathrm{cm} ) high (ii) the height of a pole which casts a shadow 5 m long. | 8 |

25 | If 18 pumps can raise 2170 tonnes of water in 10 days, working 7 hours a day then in how many days will 16 pumps raise 1736 tonnes of water, working 9 hours a day? ( A cdot 6 ) B. 7 ( c cdot 8 ) D. | 8 |

26 | Which of the following is the example of direct proportion? A. Number of mangoes in a bag and weight of the bag. B. Speed goes up, travel times goes down c. More the number of men lesser the time taken to complete it. D. None of these. | 8 |

27 | At a party, 8 bottles of soft drink are served for every batch of 5 children. How many bottles would be served if 40 children were present at the party? | 8 |

28 | A stone is dropped into a well and the report of the stone striking the bottom is heard 7.7 seconds after it is dropped. Assume that the stone falls ( 16 t^{2} m ) in ( t ) seconds and that the velocity of sound is 1,120 per second. The depth of the well is: ( mathbf{A} cdot 784 mathrm{m} ) в. ( 342 mathrm{m} ) ( c .1568 mathrm{m} ) D. ( 156.8 mathrm{m} ) E. none of these | 8 |

29 | A work is done by 10 workers in 6 hours? How many workers will be required to do the same work in 4 hrs? A . 10 B . 15 c. 20 D. None of these | 8 |

30 | If the thickness of a pile of 12 cardboards is ( 35 mathrm{mm} ), find the thickness of a pile of 294 cardboards. | 8 |

31 | A worker is paid Rs 200 for 8 days work. If he works for 20 days, how much will he get? | 8 |

32 | Following are the car parking charges near railway station upto ( 4 mathrm{hrs} quad ) Rs 60 ( mathbf{8} ) hrs ( quad boldsymbol{R} boldsymbol{s} mathbf{1 0 0} ) ( mathbf{1 2} ) hrs ( quad boldsymbol{R} boldsymbol{s} mathbf{1 4 0} ) ( mathbf{2 4} ) hrs ( quad boldsymbol{R} boldsymbol{s} mathbf{1 8 0} ) Check if the parking charges are in direct proportion to the parking time. | 8 |

33 | The number of workers increased the days to complete the work decreased.”is example of A. Inverse ratio B. Direct ratio C. Both of A and B D. none of above | 8 |

34 | A worker is paid Rs 210 for 6 days work. If his total income of the month is Rs ( 875, ) for how many days did he work? | 8 |

35 | If the cost of ( 93 mathrm{m} ) of a certain kind of plastic sheet is Rs ( 1395, ) then what would it cost to buy ( 105 mathrm{m} ) of such plastic sheet? | 8 |

36 | Which of the following are in inverse proportion? This question has multiple correct options A. The number of workers on a job and the time to complete the job. B. The time taken for a journey and the distance travelled in a uniform speed. C. Area of cultivated land and the crop harvested. D. The time taken for a fixed journey and the speed of the vehicle. E. The population of a country and the area of land per person. | 8 |

37 | A bus travels ( 120 mathrm{km} ) in 4 hrs The distance that can be travelled by the bus in 6 hrs is ( _{-} ) ( mathbf{A} cdot 18 mathrm{km} ) B. 140 km ( c .180 mathrm{km} ) D. 120 km | 8 |

38 | A man gets ( R s .7920 ) for working 48 hours a week. How much does he get when he works 36 hours a week? A. ( R s .7150 ) в. ( R s .5940 ) c. ( R s .6660 ) D. Rs. 4000 | 8 |

39 | In a Television game show, the prize money of Rs 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?? Number of winners Prize of each 1,00,000 50,000 winner (in Rs) | 8 |

40 | 55. Three taps A, B and C can fill a tank in 12, 15 and 20 hours re- spectively. IfA is open all the time and B and C are open for one hour each alternatively, the tank will be full in : (1) 6 hours (2) 6 hours (3) 7 hours (4) 7 hours | 8 |

41 | A car can finish a certain journey in 10 hours at the speed of ( 48 mathrm{km} / mathrm{hr} ). By how much should its speed be increased so that it may take only 8 hours to cover the same distance ? (in km/hr) | 8 |

42 | 53. If A: B= 2:1 and A: C= 1:3, then A:B:C is (1) 1:3:2 (2) 1:2:6 (3) 3:2:1 (4) 2:1:6 | 8 |

43 | A fist with a mass of 3 kg causes a fishing pole to bend ( 9 mathrm{cm} . ) If the amount of bending varies directly as the mass, how much will the pole bend for a ( 2 k g ) fish ? | 8 |

44 | f ( 20: 28=x: 7=10: y ) The values of ( x ) and ( y ) in the box respectively are A .5,14 в. 14,5 ( c .8,10 ) D. 10,8 | 8 |

45 | 63. Pipes P and 9 can fill a tank in 10 and 12 hours respectively and C can empty it in 6 hours. If all the three are opened at 7 a.m., at what time will one-fourth of the tank be filled ? (1) 10 a.m. (2) 10 p.m. (3) 11 p.m. (4) 11 a.m. | 8 |

46 | The cost of 97 metre of cloth is Rs 242.50. What length of this can be purchased for Rs ( 302.50 ? ) | 8 |

47 | If ( x & y ) are in inverse proportion then find proportionality constant at ( boldsymbol{x}= ) ( mathbf{3}, boldsymbol{y}=mathbf{2} ) A . 4 B. 5 ( c .6 ) D. | 8 |

48 | ( A, B ) and ( C ) can finish a job working alone in 72,24 and 36 days respectively In how many days they can finish the job if they worked together? A . 12 B. 9 c. 15 D. 18 | 8 |

49 | 64. Two natural numbers are in the ratio 3 : 5 and their product is 2160. The smaller of the num- bers is (1) 36 (2) 24 (3) 18 (4) 12 | 8 |

50 | Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for ( 72 mathrm{km} ). What would be her distance covered in the map? | 8 |

51 | The line ( A D ) is divided in the ratio of ( A B: B C: C D=1: 3: 4 . ) If ( A B= ) ( 0.8 mathrm{cm}, ) calculate the length of ( A D ) A . ( 3.5 mathrm{cm} ) B. ( 6.4 mathrm{cm} ) c. ( 5.89 mathrm{cm} ) D. ( 6.5 mathrm{cm} ) | 8 |

52 | Which of the following are in inverse proportion? (i) The number of workers on a job and the time to complete the job. (ii) The time taken for a journey and the distance travelled in a uniform speed. (iii) Area of cultivated land and the crop harvested. (iv) The time taken for a fixed journey and the speed of the vehicle. (v) The population of a country and the area of land per person. | 8 |

53 | 11 men can dig ( 6 frac{3}{4} ) metre long trench in one day. How many men should be employed for digging 27 metre long trench of the same type in one day? | 8 |

54 | cost of 10 mangoes is Rs. 100 The cost of 18 mangoes is A . Rs. 18 B. Rs. 108 c. Rs. 200 D. Rs. 180 | 8 |

55 | 53. Two numbers are in ratio 5 : 8. If their difference is 48, then the smaller number is (1) 80 (2) 96 (3) 128 (4) 64 | 8 |

56 | 4 men or 6 women earn Rs 360 in one day. Find how much will 6 men and 4 women earn in one day? A . Rs 780 B. Rs 720 c. Rs 760 D. Rs 740 | 8 |

57 | ff ( y ) varies inversely as ( x, ) and ( y=9 ) when ( x=2, ) find ( y ) when ( x=3 ) | 8 |

58 | A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle? | 8 |

59 | In a Television game show, the prize money of Rs 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? Number of winners Prize for each [ begin{array}{rr} 50,000 \ , 00,000 end{array} ] winner (in Rs.) | 8 |

60 | Which of the following ( a & b ) are in direct proportion? A ( cdot a=frac{2}{b} ) В. ( a=2 b ) c. ( a=b^{3} ) D. ( a=frac{1}{b^{2}} ) | 8 |

61 | 51. The cost of making an article is divided between materials, la- bour and overheads in the ratio 3:4:2. If the cost of material 33.60, the cost of article is (1) 100.80 (2) 11.20 (3) 44.80 (4) 22.40 | 8 |

62 | 18 men can reap a filed in 35 days. For reaping the same filed in 15 days, how many men are required? | 8 |

63 | A fort is provisioned for 42 days. After 10 days, a reinforcement of 200 men arrives and the food will now last only 24 days. How many men were there in the fort? A .200 в. 600 ( c .500 ) D. 300 | 8 |

64 | f ( a, b, c, d ) are in continued proportion, prove that ( (a+d) b+c)-(a+c)(b+d)= ) ( (b-c)^{2} ) | 8 |

65 | The cost of 2 meter cloth is ( 10 . ) Find the ( operatorname{cost} ) of ( 100 m ) cloth. A . 400 в. 500 ( c .1000 ) D. 1500 | 8 |

66 | A work – force of 420 men with a contractor can finish a certain piece of work in 9 months. How many extra men must he employ to complete the job in 7 months? | 8 |

67 | If ( boldsymbol{a}: boldsymbol{b}=mathbf{5}: mathbf{9} ) and ( boldsymbol{b}: boldsymbol{c}=boldsymbol{4}: mathbf{7} ) find ( boldsymbol{a}: ) ( boldsymbol{b}: boldsymbol{c} ) This question has multiple correct options A ( cdot 5: 9: frac{63}{4} ) B. 20: 63: 36 ( mathbf{c} cdot 4: 36: 63 ) D. 20: 36: 63 | 8 |

68 | Eight oranges can be bought for Rs 10.40, then how many more oranges can be bought for Rs ( 16.90 ? ) A. 5 oranges B. 3 oranges c. 7 oranges D. 2 oranges | 8 |

69 | 14 apples cost Rs. 140 The cost of 1 apple is A. Rs. 10 B. Rs. 8 c. Rs. 4 D. Rs. 14 | 8 |

70 | If 36 men can do a piece of work in 25 days, in how many days will 15 men do it ( ? ) | 8 |

71 | Which is example of inverse proportion? A. Length of edge of square & its area B. Speed and time taken C. Length of edge of square ( & ) its perimeter D. Quantity of pencils & total cost | 8 |

72 | State true or false: Following are the car parking charges near a railway station upto 4 hours Rs 60 8 hours Rs 100 12 hours Rs 140 24 hours Rs 180 Hence, the parking charges are in direct proportion to the parking time. A. True B. Fals | 8 |

73 | Rohit bought 12 registers for Rs 156, find the cost of 7 such registers. (in Rs.) | 8 |

74 | If ( a ) is directly proportional to ( b ) and ( b ) is inversely proportional to ( c . ) Then what is the proportionality between ( a ) and ( c ? ) A . Direct B. Inverse c. sometimes direct sometimes inverse D. Can’t be determined | 8 |

75 | Four pipes can fill a tank in 70 min. How Iong will it take to fill the tank by 7 pipes? A . 20 min B. 35 min ( c .40 ) min D. None of these | 8 |

76 | D 10 – Aman can row at 8 kmph in still water. If the river is running at 2 kmph, it takes him 48 minutes to row to a place and back. How far is the place? • 1 100 | 8 |

77 | 35 workers can build a house in 16 days. How many days will 28 workers working at the same rate take to build the same house? A. 16 days в. 28 days c. 20 days D. 10 days | 8 |

78 | Find inverse proportionaly constant if ( x ) and ( y ) are in inverse proportion. [ boldsymbol{x} quad mathbf{9} quad boldsymbol{6} quad boldsymbol{3} quad boldsymbol{1} ] begin{tabular}{l} 6 \ hline end{tabular} ( y quad 2 quad 3 ) ( mathbf{A} cdot mathbf{9} ) B. 18 c. 27 D. 30 | 8 |

79 | If light can travel 31 times around the world in 4 seconds, how many times can it circle the world in 10 seconds. A. 124 times в. ( 66 frac{1}{2} ) times c. ( quad 82 frac{1}{2} ) times D. 77.5 times | 8 |

80 | ( boldsymbol{m}: boldsymbol{n} ) | 8 |

81 | On a scale of map, ( 0.6 mathrm{cm} ) represents 6.6km. If the distance between the points on the map is ( 80.5 mathrm{cm}, ) the actualdistance between these points is ( mathbf{A} cdot 9 mathrm{km} ) в. ( 72.5 mathrm{km} ) c. ( 190.75 mathrm{km} ) D. ( 885.5 mathrm{km} ) | 8 |

82 | ( begin{array}{ccccc}boldsymbol{x} & mathbf{2} & boldsymbol{4} & mathbf{2 0} & mathbf{1 5} \ y & 3 & 7 & 10 & 12 \ z & 10 & 5 & 1 & 4 / 3end{array} ) Observe the table and find the quantities which are in inverse proportion A. ( x ) and ( y ) B. ( x ) and ( z ) ( mathbf{c} cdot y ) and ( z ) D. None of the above | 8 |

83 | Which is an example of direct proportion? A. More working hours, more earning B. More speed of car, less time taken C. More no. of workers, less time taken D. Less the age of person, more active he is | 8 |

84 | 56. A does 20% less work than B. If A can complete a piece of work in 7 hours, then B can do it in (1) 10 hours (3) 6 hours (2) 4 hours (4) 8 hours | 8 |

85 | Three spraying machines working together can finish painting a house in 60 minutes. How long will it take for 5 machines of the same capacity to do the same job ?(in minutes) | 8 |

86 | The cost of 5 tables and 6 chairs is Rs. ( 2884 . ) What is the cost of 15 tables and 18 chairs? A. ( R s .3300 ) в. ( R s .7332 ) c. ( R s .5600 ) D. ( R s .8652 ) | 8 |

87 | In 15 days, the earth picks up ( 1.2 times 10^{8} ) kg of dust from the atmosphere. In how many days it will pick up ( 4.8 times 10^{8} mathrm{kg} ) of dust? | 8 |

88 | Kamal can do a piece of work in 12 day. -hich Debashis can fin- ish in 10 days. If they work at it on alternate days with Debashis beginning in how many days, the work will be finished ? (1) 10 days (2) 10 days 3 11 days (4 11 days | 8 |

89 | Complete the following table if ( boldsymbol{x} propto boldsymbol{y} ) [ x ] ( begin{array}{lllll}1 & 2 & 3 & – & 5end{array} ) ( 4 quad 8 ) 16 ( – ) ( y ) 1 | 8 |

90 | How many men must be engaged to do a piece of work in 16 days which 24 men can do in 40 days? | 8 |

91 | In library 136 copies of a certain book require a shelf-length of 3.4 metre. How many copies of the same book would occupy a shelf-length of 5.1 meters? | 8 |

92 | 64. 36 workers can do a piece of work in 55 days. 66 workers can do twice of this work in (1) 33 days (2) 40 days (3) 60 days (4) 44 days | 8 |

93 | In a hostel of 50 girls, there are food provisions for 40 days. If 30 more girls join the hostel, how long will these provisions last ? (in days) | 8 |

94 | If ( frac{a}{b}-frac{c}{d}=0 ) and ( b c=7, ) then determine the true statement among the following. A. a and b are directly proportional. B. a and c are inversely proportional. c. a and d are inversely proportional. D. b and c are directly proportional. E. c and d are inversely proportional. | 8 |

95 | Mark the correct alternative of the following. Two numbers are in the ration 3: 5 and their sum is ( 96 . ) The larger number is? A . 36 B. 42 c. 60 D. 70 | 8 |

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