With x and y in direct proportion, x = 6 against y = 18 pushes y to 30 when x = 10, while inverse proportion turns x = 4, y = 12 into y = 8 at x = 6, so this sheet contrasts the two scaling rules. Speed and time for a fixed distance form an inverse example.
Key Takeaways
Direct proportion: x = 6 with y = 18 gives y = 30 when x = 10 (Q1).
Inverse proportion: x = 4 with y = 12 gives y = 8 when x = 6 (Q2).
Speed and time for a fixed distance form an inverse example.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.If x and y vary directly, and x = 6 when y = 18, find y when x = 10:
(a) 20(b) 25(c) 30(d) 36
2.If x and y vary inversely, and x = 4 when y = 12, find y when x = 6:
(a) 6(b) 8(c) 10(d) 18
3.Which of the following is an example of inverse proportion?
(a) Speed and time for fixed distance(b) Speed and distance for fixed time(c) Cost and quantity(d) Workers and work done
4.If 5 workers can build a wall in 12 days, 6 workers can build it in:
(a) 8 days(b) 10 days(c) 12 days(d) 14 days
5.x ∝ y implies:
(a) xy = k(b) x/y = k(c) x = k/y(d) x + y = k
6.If 15 oranges cost ₹90, the cost of 25 oranges is:
(a) ₹120(b) ₹130(c) ₹140(d) ₹150
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.If 6 kg of sugar costs ₹240, find the cost of 15 kg of sugar.
8.A car travels 180 km in 3 hours. How far will it travel in 5 hours at the same speed?
9.If 8 pipes can fill a tank in 9 hours, how long will 12 pipes take to fill the same tank?
10.A machine prints 480 pages in 6 minutes. How many pages will it print in 15 minutes?
11.If 25 men can do a piece of work in 18 days, how many men are needed to finish it in 15 days?
12.Check if the following is a direct proportion: x = 2, 4, 6, 8 and y = 6, 12, 18, 24.
13.If a ∝ b and a = 10 when b = 4, find a when b = 14.
14.A map scale is 1 cm : 50 km. If two cities are 7.5 cm apart on the map, find the actual distance.
Section C: Word Problems (3 Marks Each)
Apply the concepts to solve real-life problems.
15.A farmer has enough food to feed 20 animals for 6 days. How long will the food last if 10 more animals join?
16.If 12 workers can build a wall in 20 days, how many days will 15 workers take?
17.A bus travels at 40 km/h and reaches its destination in 3 hours. How fast must it travel to reach in 2.5 hours?
18.The shadow of a 5 m tall pole is 2 m long. At the same time, the shadow of a tree is 6.4 m. Find the height of the tree.
19.A garrison of 120 men has provision for 30 days. After 10 days, 30 more men arrive. How long will the remaining food last?
20.The cost of 18 books is ₹630. How many books can be bought for ₹1,225?
Answer Key
1. c) 30
2. b) 8
3. a) Speed and time for fixed distance
4. b) 10 days
5. b) x/y = k
6. d) ₹150
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End of Worksheet
People Also Ask
If x and y are directly proportional, and x = 6 when y = 18, what is y when x = 10?
30, option (c) in this worksheet (Q1).
If x and y vary inversely, and x = 4 when y = 12, what is y when x = 6?
8, option (b) in this worksheet (Q2).
What is an example of inverse proportion?
Speed and time for a fixed distance, from the answer key on this page.
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