Proportional Reasoning - 1 | IT

Question 1

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

Question diagram 1
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Solution
Understand the Question
  • Two images look similar if they have the same shape and maintain the same height-to-width ratio (proportions), regardless of size.
  • If an image is stretched either horizontally or vertically, its aspect ratio changes and the image looks distorted or different.

Step 1 · Analyze Reference Image A

Image A displays the tiger in its normal, undistorted form, serving as the standard reference for shape and proportions.Diagram 1

Step 2 · Compare Image B with Image A

The tiger in Image B appears wider and shorter. It has been stretched horizontally, changing its height-to-width ratio.Diagram 2

Step 3 · Compare Image C with Image A

Image C is a smaller version of Image A. The shape and proportions are maintained exactly without any distortion.Diagram 3

Step 4 · Compare Image D with Image A

Image D is an enlarged version of Image A. The shape and proportions are maintained exactly without any distortion.Diagram 4

Step 5 · Compare Image E with Image A

The tiger in Image E appears taller and thinner. It has been stretched vertically, altering its height-to-width ratio.Diagram 5

Step 6 · Group Similar and Different Images

  • Similar Images: A, C, and D maintain the original proportions and shape.
  • Different Images: B (stretched horizontally) and E (stretched vertically) have distorted proportions.
Answer
  • Similar images: A, C, and D
  • Different images: B and E
Common Mistakes
  • Confusing Size with Shape: Thinking that a smaller or larger image (like C or D) is "different". If the height-to-width ratio is unchanged, the images remain geometrically similar.
  • Ignoring Directional Stretch: Not distinguishing between horizontal stretching (Image B) and vertical stretching (Image E).

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 60:4060 : 40 (image A) to get 90:6090 : 60 (image D)?

Q4

In my school, there are 5 teachers and 170 students. The ratio of teachers to students in my school is 5:1705 : 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 mL15\text{ mL} of coffee decoction with 35 mL35\text{ mL} of milk to make filter coffee (ratio 15:3515 : 35). For 'stronger' coffee, he mixes 20 mL20\text{ mL} of decoction with 30 mL30\text{ mL} of milk (ratio 20:3020 : 30).

Q. Why is this coffee stronger?

Q10

Context: Manjunath usually mixes 15 mL15\text{ mL} of coffee decoction with 35 mL35\text{ mL} of milk to make filter coffee (ratio 15:3515 : 35). For 'lighter' coffee, he mixes 10 mL10\text{ mL} of coffee and 40 mL40\text{ mL} of milk, making the ratio 10:4010 : 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 6:1806 : 180. The ratio of their prices is 2:1542 : 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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