Grade 8 Inverse Proportions

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1 ID : pk-8-inverse-proportions [1] Grade 8 Inverse Proportions For more such worksheets visit Answer t he quest ions (1) Samira can complete a task in 30 minutes, while Rashida can complete the same task in 6 minutes. How long will it take to complete the task, if both Samira and Rashida work together? (2) Pump A can f ill a tank in 60 minutes, while pump B can f ill the same tank in 40 minutes. Both pumps are turned on together to f ill the empty tank, but when tank became half f ull, pump B stops working and rest of the tank is f illed by pump A only. How long it took to f ill the tank? (3) Af sheen and Naeem can together do a work in 12 minutes. If Af sheen alone can do the work in 21 minutes, how long will it take f or Naeem to do it alone? (4) If 6 men can paint a building in 20 days, how many men are required to do this in 5 days. (5) There are f ew taps and holes in tank. Each tap can f ill empty tank in 21 minutes, while each hole can empty a f ull tank in 28 minutes. If there are 4 taps and 3 holes, how long would it take to f ill empty tank? (6) Wasif and Nawaz can f inish a work in 10 and 5 days respectively. If this work is done by both of them on alternate days (starting with Wasif ), how long will it take f or them to f inish the work? Choose correct answer(s) f rom given choice (7) 3 workers can build a 60 meter tower in 5 days. At the same rate, how long will it take f or 5 workers to build a 80 meter tower? a. 3 days b. 2 days c. 4 days d. 6 days (8) Two taps A and B can f ill a water tank in 20 and 10 hours respectively. If they are turned up alternatively f or one hour each (staring with tap B). Find the time taken to f ill the tank. a. 14 hours b. 15 hours c. 12 hours d. 13 hours (9) Train X takes 20 hours to travel f rom station A to station B, while train Y takes 5 hours to travel f rom station B to station A. If train X and Y starts at same time f rom stations A and B respectively, af ter what time will they cross each other? (Assume trains travel with unif orm speed) a. 7 hours b. 10 hours c. 4 hours d. 2 hours (10) Tap A can f ill a tank in 3 hours, while tap B can f ill the same tank in 6 hours. If both taps are open together, how long will it take to f ill an empty tank? a. 4 hours b. 1 hours c. 2 hours d. 0 hours

2 ID : pk-8-inverse-proportions [2] (11) Tap A can f ill a tank in 4 hours, while tap B can empty the f ull tank in 6 hours. If both taps are open together, how long will it take to f ill an empty tank? a. 15 hours b. 11 hours c. 12 hours d. 14 hours (12) Pakeeza and Af zal together can do a work in 60 days, but if Badar also helps them they can f inish it in 24 days only. How long would it take if Badar has to do it alone? a. 39 days b. 38 days c. 40 days d. 43 days (13) If a man can do a work in 16 days, and woman can do the same work in 8 days, in how many days 4 men and 2 women can do the same work. a. 2 days b. 4 days c. 0 days d. 1 days Fill in the blanks (14) A water tank has two types of taps (type-a and type-b). A tap of type-a can f ill the tank in 24 minutes, while a tap of type-b can f ill the same tank in 36 minutes. If there are 2 type-a taps and 3 type-b taps that can be used to f ill the tank, then an empty tank can be f illed in minutes. (15) A B If bear can walk f rom A to B in 21 minutes, while mouse can walk f rom B to A in 28 minutes. If both start walking at same time, they will cross each other af ter minutes Edugain ( All Rights Reserved Many more such worksheets can be generated at

3 Answers ID : pk-8-inverse-proportions [3] (1) 5 minutes We know that f or Samira, it takes 30 minutes to complete a task. So in 1 minute it will complete 1/30 of the task. So in 'x' minutes it will complete x/30 of the task. We know that f or Rashida, it takes 6 minutes to complete a task. So in 1 minute it will complete 1/6 of the task. So in 'x' minutes it will complete x/6 of the task Since both Samira and Rashida together complete the task so x/30 + x/6 = 1 (1 ref erring to 1 complete task) Solving this we get x = 5 minutes (2) 42 minutes Pump A can f ill the tank in 60 minutes. So in 1 minute it would f ill 1/60 of the tank. So in 'x' minutes it would f ill x/60 of the tank. Similarly, Pump B can f ill the tank in 40 minutes. So in 1 minute it would f ill 1/40 of the tank. So in 'x' minutes it would f ill x/60 of the tank. Here when both the pumps are open, they together f ill only half of the tank. So the equation f ormed would be x/60 + x/40 = 1/2 Solving this we get x = 12 Step 5 We know that the remaining half tank was f illed by pump A. So if pump A takes 60 minutes to f ill the whole tank, then it would take 60/2 minutes to f ill half of the tank Step 6 So the total time taken to f ill the tank is /2 = 42 minutes.

4 (3) 28 minutes ID : pk-8-inverse-proportions [4] We know that f or Af sheen, it takes 21 minutes to complete a work. So in 1 minute it will complete 1/21 of the work. So in 'x' minutes it will complete x/21 of the work. Let us consider that f or Naeem, it takes 'y' minutes to complete a work. So in 1 minute it will complete 1/y of the work. So in 'x' minutes it will complete x/y of the work Since both Af sheen and Naeem together complete the work so x/21 + x/y = 1 (1 ref erring to 1 complete work ) Af sheen and Naeem can together do a work in 12 minutes. So we let our 'x' be equal to 12. So now our eqaution f ormed is 12/ /y = 1. Step 5 Solving this we get y = 28. So it takes Naeem 28 minutes to complete the work individually. (4) 24 It takes 20 days f or 6 men to paint a building In 1 day it will take 6*20 men to paint a building For 5 days, it will take 6*20 / 5 men to paint a building So the answer is 24 men.

5 (5) 12 minutes ID : pk-8-inverse-proportions [5] It takes one tap 21 minutes to f ill 1 tank. So in 'x' minutes it f ills x/21 of the tank So with 4 taps, it will f ill (4 * x )/21 of the tank. It takes one hole 28 minutes to f ill 1 tank. So in 'x' minutes it empties x/28 of the tank So with 3 holes, it will empty (3 * x )/28 of the tank. So the equation f ormed is (4 * x )/21 - (3 * x )/28 = 1 (subtraction is being done because we have to remove the quantity that is being emptied by the holes ) Solving this equation we get x = 12 minutes (6) 7 days Wasif takes 10 days to f inish a work. So in 1 day it f inishes 1/10 of the work. Nawaz takes 5 days to f inish a work. So in 1 day it f inishes 1/5 of the work. Since the work is done on alternate days, so one day 1/10 of the work is done, and the second day 1/5 of the work is done. We have to f ind out the number of days required to f inish the work. Step 5 So 1/10 + 1/5 + 1/10 + 1/ = 1 When this value equals to one, we get the number of days the work was completed in. Step 6 So here work was completed in 7 days

6 (7) c. 4 days ID : pk-8-inverse-proportions [6] Since work done by 3 workers in 5 days = 60 meter Work done by 3 workers in one day = 60/5 = 12 meter Work done by one worker in one day = 12/3 = 4 meter Work done by 5 workers in one day = 4 5 = 20 meter Since 20 meter tower is done by 5 workers in one day 80 meter tower will be done by 5 workers in 80/20 = 4 days (8) d. 13 hours Tap A takes 20 hours to f ill a water tank. So in 1 hour it f ills 1/20 of the tank. Tap B takes 10 hours to f ill a water tank. So in 1 hour it f ills 1/10 of the tank. Since the tank is f illed by each tap in alternate hours, so in one hour 1/20 of the tank is f illed, and the second hour 1/10 of the tank is f illed. We have to f ind out the number of hours required to f ill the whole tank. Step 5 So 1/20 + 1/10 + 1/20 + 1/ = 1 When this value equals to one, We get the number of hours the tank was f illed in. Step 6 So here the tank was f ull in 13 hours

7 (9) c. 4 hours ID : pk-8-inverse-proportions [7] Train X takes 20 hours to reach f rom A to B that is 1 side. So in 1 hour it will reach 1/20 of the distance. So in 'x' hours it will reach x/20 of the distance. Train Y takes 5 hours to reach f rom B to A that is 1 side. So in 1 hour it will reach 1/5 of the distance. So in 'x' hours it will reach x/5 of the distance. So the equation f ormed is x/20 + x/5 = 1 (When both trains will meet at a point, so the total distance between the two stations is covered ) Solving this we get x = 4 hours (10) c. 2 hours We know that f or A, it takes 3 hours to f ill 1 tank. So in 1 hour it will f ill 1/3 of the tank. So in 'x' hours it will f ill x/3 of the tank We know that f or B, it takes 6 hours to f ill 1 tank. So in 1 hour it will f ill 1/6 of the tank. So in 'x' hours it will f ill x/6 of the tank Since both taps are used to f ill the tank so x/3 + x/6 = 1 (1 ref erring to 1 f ull tank ) Solving this we get x = 2 hours

8 (11) c. 12 hours ID : pk-8-inverse-proportions [8] If you look at the question caref ully, you will notice that Tap A can f ill a tank in 4 hours, while tap B can empty the f ull tank in 6 hours. If both taps are open together, then the time it will take to f ill an empty tank is equal to the LCM of the time in which Tap A can f ill a tank and tap B can empty the f ull tank. Calculating the LCM of 4 and 6. All prime f actors of 4: is a factor of is a factor of = 2 2 All prime f actors of 6: is a factor of is a factor of = 2 3 Step 5 Now the LCM of 4 and 6 is = = 12 Step 6 Theref ore the time it will take to f ill an empty tank = 12 hours

9 (12) c. 40 days ID : pk-8-inverse-proportions [9] Pakeeza and Af zal together can do a work in 60 days. So we consider it as one unit. So if they can complete a work in 60 days,then in 'x' days they can complete x/60 of the work. Let say Badar can complete a work in 'y' days. So in 'x' days, x/y of the work can be done. If Pakeeza, Af zal and Badar do the work together they complete it in 24 days. So the equation f ormed is x/60 + x/y = 1. Here x = 24. Now the equation is 24/ /y = 1. Solving f or y we get y = 40. So Badar completes the work individually in 40 days. (13) a. 2 days A man can do a work in 16 days. So in 1 day, he could do 1/16 of the work. So 4 men in 1 day could do 4/16 of the work. So in 'x' days x/16 of the work would be done. So 4 men in 'x'days could do (4*x)/16 of the work. A woman can do a work in 8 days. So in 1 day, she could do 1/8 of the work. So in 'x' days x/8 of the work would be done. So 2 women in 'x'days could do (2*x)/8 of the work. So the equation f ormed would be (4*x)/16 + (2*x)/8 = 1 Solving this we get x = 2 So the work can be completed in 2 days

10 (14) 6 ID : pk-8-inverse-proportions [10] We know that f or A, it takes 24 minutes to f ill 1 tank. So in 1 minute it will f ill 1/24 of the tank. So in 'x' minutes it will f ill x/24 of the tank. We know that f or B, it takes 36 minutes to f ill 1 tank. So in 1 hour it will f ill 1/36 of the tank. So in 'x' minutes it will f ill x/36 of the tank. Since 2 taps of A and 3 taps of B are used to f ill the tank so (2*x)/24 + (3*x)/36 = 1 (1 ref erring to 1 f ull tank ) Solving this we get x = 6 minutes. (15) 12 A bear takes 21 minutes to reach f rom A to B that is 1 side. So in 1 minute it will reach 1/21 of the distance. So in 'x' minutes it will reach x/21 of the distance. A mouse takes 28 hours to reach f rom B to A that is 1 side. So in 1 hour it will reach 1/28 of the distance. So in 'x' minutes it will reach x/28 of the distance. So the equation f ormed is x/21 + x/28 = 1 (When both trains will meet at a point, so the total distance between the two stations is covered ) Solving this we get x = 12 minutes