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The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number? 
  • a)
    3 
  • b)
    4
  • c)
     9 
  • d)
    Cannot be determined
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The difference between a two-digit number and the number obtained by i...
Let the ten's digit be x and unit's digit be y. 
Then, (10x + y) - (10y + x) = 36 
⇒ 9(x - y) = 36 
⇒ x - y = 4
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Most Upvoted Answer
The difference between a two-digit number and the number obtained by i...
Given:
- The equation of the circle is x^2 + y^2 = 11.
- A lattice point is a point in which both x and y are integers.

To find:
- The number of lattice points in the interior of the circle.

Explanation:
To determine the number of lattice points in the interior of the circle, we need to analyze the equation and understand the properties of lattice points.

Properties of Lattice Points:
1. A lattice point has both x and y coordinates as integers.
2. A lattice point lies on the circumference of the circle if the equation of the circle is satisfied.
3. A lattice point lies in the interior of the circle if the equation of the circle is satisfied and the point is not on the circumference.

Approach:
We can use a combination of algebraic and geometric methods to determine the number of lattice points in the interior of the circle.

1. Identify the range of values for x and y:
- Since x^2 + y^2 = 11, the maximum possible value for both x and y is √11.
- The minimum possible value for both x and y is -√11.
- Therefore, the range of values for x and y is -√11 ≤ x, y ≤ √11.

2. Visualize the circle and lattice points:
- Plotting the circle on a coordinate plane, we can visualize the possible lattice points.
- By observing the graph, we can identify the lattice points on or within the circle.

3. Analyze the quadrant-wise distribution of lattice points:
- Since the circle is symmetric with respect to the x and y axes, we can focus on one quadrant.
- By analyzing the lattice points in one quadrant, we can determine the total number of lattice points in all four quadrants.

4. Count the lattice points:
- By identifying the lattice points in one quadrant and considering symmetry, we can count the total number of lattice points in all four quadrants.

Counting Lattice Points:
By analyzing the circle and considering the properties of lattice points, we can count the lattice points in each quadrant:

1. Quadrant I:
- In this quadrant, both x and y are positive.
- Counting the lattice points in this quadrant, we find that there are 9 lattice points: (1, 3), (2, 2), (3, 1), (1, 2), (2, 1), (1, 1), (3, 2), (2, 3), (3, 3).

2. Quadrant II:
- In this quadrant, x is negative and y is positive.
- Counting the lattice points in this quadrant, we find that there are 9 lattice points: (-1, 3), (-2, 2), (-3, 1), (-1, 2), (-2, 1), (-1, 1), (-3, 2), (-2, 3), (-3, 3).

3. Quadrant III:
- In this quadrant, both x and y are negative.
- Counting the lattice points in this quadrant, we find that there are 9 lattice points: (-1, -3), (-2, -2),
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Community Answer
The difference between a two-digit number and the number obtained by i...
Let the ten's digit be x and unit's digit be y. 
Then, (10x + y) - (10y + x) = 36 
⇒ 9(x - y) = 36 
⇒ x - y = 4
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Directions: Read the passage and answer the questions that follow:There are two parties to every observation---the observed and the observerWhat we see depends not only on the object looked at, but on our own circumstances---position, motion, or more personal idiosyncrasies. Sometimes by instinctive habit, sometimes by design, we attempt to eliminate our own share in the observation, and so form a general picture of the world outside us, which shall be common to all observers. A small speck on the horizon of the sea is interpreted as a giant steamer. From the window of our railway carriage we see a cow glide past at fifty miles an hour, and remark that the creature is enjoying a rest. We see the starry heavens revolve round the earth, but decide that it is really the earth that is revolving, and so picture the state of the universe in a way which would be acceptable to an astronomer on any other planet.The first step in throwing our knowledge into a common stock must be the elimination of the various individual standpoints and the reduction to some specified standard observer. The picture of the world so obtained is none the less relative. We have not eliminated the observer's share; we have only fixed it definitely.To obtain a conception of the world from the point of view of no one in particular is a much more difficult task. The position of the observer can be eliminated; we are able to grasp the conception of a chair as an object in nature---looked at all round, and not from any particular angle or distance. We can think of it without mentally assigning ourselves some position with respect to it. This is a remarkable faculty, which has evidently been greatly assisted by the perception of solid relief with our two eyes. But the motion of the observer is not eliminated so simply. We had thought that it was accomplished; but the discovery that observers with different motions use different space- and time-reckoning shows that the matter is more complicated than was supposed. It may well require a complete change in our apparatus of description, because all the familiar terms of physics refer primarily to the relations of the world to an observer in some specified circumstances.Whether we are able to go still further and obtain a knowledge of the world, which not merely does not particularise the observer, but does not postulate an observer at all; whether if such knowledge could be obtained, it would convey any intelligible meaning; and whether it could be of any conceivable interest to anybody if it could be understood---these questions need not detain us now. The answers are not necessarily negative, but they lie outside the normal scope of physics.The circumstances of an observer which affect his observations are his position, motion and gauge of magnitude. More personal idiosyncracies disappear if, instead of relying on his crude senses, he employs scientific measuring apparatus. But scientific apparatus has position, motion and size, so that these are still involved in the results of any observation. There is no essential distinction between scientific measures and the measures of the senses. In either case our acquaintance with the external world comes to us through material channels; the observer's body can be regarded as part of his laboratory equipment, and, so far as we know, it obeys the same laws. We therefore group together perceptions and scientific measures, and in speaking of “a particular observer” we include all his measuring appliances.Position, motion, magnitude-scale---these factors have a profound influence on the aspect of the world to us. Can we form a picture of the world which shall be a synthesis of what is seen by observers in all sorts of positions, having all sorts of velocities, and all sorts of sizes?As per the passage, the author believes that

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The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?a)3b)4 c)9d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?
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