Proportional Reasoning - 1 | IT

Question 1

Q. Which images look similar and which ones look different?

Question diagram 1
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Solution

IT-1

Chapter: PROPORTIONAL REASONING - 1
Class: 8 (Class 8)
Category: in_text


Question

Q. Which images look similar and which ones look different?

Question diagram(s):

Question diagram


We need to observe the shape of the tiger in each image and see if its proportions are maintained or distorted.

Step 1 — Observing Image A

Let us look at Image A. The tiger in this image looks normal. We can use this as our reference for the correct shape.

Diagram 1

Step 2 — Comparing Image B with Image A

Now, let us compare Image B with Image A. The tiger in Image B appears wider and shorter than in Image A. It looks like it has been stretched sideways. This means its height-width ratio has changed.

Diagram 2

Step 3 — Comparing Image C with Image A

Next, let us compare Image C with Image A. Image C is a smaller picture of the tiger. However, the tiger's shape and proportions look exactly the same as in Image A. It is just a smaller version.

Diagram 3

Step 4 — Comparing Image D with Image A

Let us compare Image D with Image A. Image D is a larger picture of the tiger. The tiger's shape and proportions still look the same as in Image A. It is just a bigger version.

Diagram 4

Step 5 — Comparing Image E with Image A

Finally, let us compare Image E with Image A. The tiger in Image E appears taller and thinner than in Image A. It looks like it has been stretched upwards. This means its height-width ratio has changed.

Diagram 5

Step 6 — Grouping similar and different images

Images A, C, and D all show the tiger with the same proportions. They maintain the original shape, just at different sizes. Images B and E show the tiger with distorted proportions. Image B is stretched horizontally, and Image E is stretched vertically.

Answer

Images that look similar: A, C, and D. These images maintain the same height-width ratio, so the tiger's shape looks normal and proportional. Images that look different: B and E. Image B looks wider or stretched horizontally. Image E looks taller or thinner, stretched vertically.

More questions in IT

Q1

Q. Which images look similar and which ones look different?

Q2

Can you check by what factors the width and height of image D change as compared to image A? Are the factors the same?

Q3

By what factor should we multiply the ratio 60 : 40 (image A) to get 90 : 60 (image D)?

Q4

In my school, there are 5 teachers and 170 students. The ratio of teachers to students in my school is 5 : 170. Count the number of teachers and students in your school. What is the ratio of teachers to students in your school? Write it below.

Q5

Is the teacher-to-student ratio in your school proportional to the one in my school?

Q6

Measure the width and height (to the nearest cm) of the blackboard in your classroom. What is the ratio of width to height of the blackboard?

Q7

Can you draw a rectangle in your notebook whose width and height are proportional to the ratio of the blackboard?

Q8

Compare the rectangle you have drawn to those drawn by your classmates. Do they all look the same?

Q9

Context: Manjunath usually mixes 15 mL of coffee decoction with 35 mL of milk to make filter coffee (ratio 15 : 35). For 'stronger' coffee, he mixes 20 mL of decoction with 30 mL of milk (ratio 20 : 30).

Q. Why is this coffee stronger?

Q10

Context: Manjunath usually mixes 15 mL of coffee decoction with 35 mL of milk to make filter coffee (ratio 15 : 35). For 'lighter' coffee, he mixes 10 mL of coffee and 40 mL of milk, making the ratio 10 : 40.

Q. Why is this coffee lighter?

Q11

The following table shows the different ratios in which Manjunath mixes coffee decoction with milk. Write in the last column if the coffee is stronger or lighter than the regular coffee.

Q12

Does the drawing look more realistic if the ratios are proportional? Why? Why not?

Q13

Puneeth’s father went from Lucknow to Kanpur in 2 hours by riding his motorcycle at a speed of 50 km/h. If he drives at 75 km/h, how long will it take him to reach Kanpur? Can we form this problem as a proportion—

Would it take Puneeth’s father more time or less time to reach Kanpur? Think about it.

Q14

Context: The volume of a sachet is 6 mL and its price is ₹2. The volume of a small bottle is 180 mL and its price is ₹154. The ratio of the volume of a sachet to a small bottle is 6 : 180. The ratio of their prices is 2 : 154.

Q. Why do you think that the ratio of the prices is not proportional to the ratio of the volumes?

Q15

Context: You have 12 countable objects or counters to share between the two of you.

Q. If you divide them equally, what is the ratio of the number of counters with each of you?

Q16

Context: You have 12 countable objects or counters to share between the two of you.

Q. If your partner gets 5 counters, how many objects will you get? What is the ratio of the counters?

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