All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
Class 12 Exam  >  Class 12 Questions  >  When a particular positive number is divided ... Start Learning for Free
SaveJoin the Discussion on the App
When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.
  • a)
    34
  • b)
    19
  • c)
    49
  • d)
    64
Correct answer is option 'B'. Can you explain this answer?
FREE This question is part of
Download PDF Attempt Test
Download PDF Attempt this Test
Most Upvoted Answer
When a particular positive number is divided by 3, the remainder is 1....
To solve this problem, we can use the concept of modular arithmetic.

Let's assume the positive number we are looking for is represented by "x".

Given that when x is divided by 3, the remainder is 1, we can write this as:
x ≡ 1 (mod 3)

Similarly, when x is divided by 5, the remainder is 4, we can write this as:
x ≡ 4 (mod 5)

We are also given that the difference between the quotients of the division is 3. This means that if we divide x by 3 and divide x by 5, and then subtract the two quotients, the result is 3. Mathematically, we can represent this as:
(x/3) - (x/5) = 3

To simplify this equation, we can find a common denominator for the two fractions:
(5x - 3x) / (3 * 5) = 3
2x / 15 = 3

Now, we can solve for x by multiplying both sides of the equation by 15:
2x = 3 * 15
2x = 45
x = 45 / 2
x = 22.5

However, the question specifically asks for a positive number. Since x is not an integer, we need to find the next positive integer that satisfies the given conditions.

The next positive integer that satisfies the conditions is 23. Let's verify this:

23 ≡ 1 (mod 3)
23 ≡ 4 (mod 5)

Now, let's check if the difference between the quotients of the division is 3:
(23/3) - (23/5) = 7.67 - 4.6 = 3.07

So, the number that satisfies all the given conditions is 23. Thus, the correct answer is option B.
Free Test
FREE
Start Free Test
Start Free Test
Community Answer
When a particular positive number is divided by 3, the remainder is 1....
Let the quotients when this number is divided by 3 and 5 be x and y respectively.
(Note that x will be greater than y as 3 is smaller than 5).
Number = 3x + 1 = 5y + 4
Given that, x – y = 3
On solving both equation we get, x = 6, y=3
Thus the number is 5 × 3 + 4= 19.
< Previous Question Next Question >
Explore Courses for Class 12 exam

Similar Class 12 Doubts

Read the following text and answer the following questions on the basis of the same:Negative Refractive Index: One of the most fundamental phenomena in optics is refraction. When a beam of light crosses the interface between two different materials, its path is altered depending on the difference in the refractive indices of the materials. The greater the difference, the greater the refraction of the beam. For all known naturally occurring materials the refractive index assumes only positive values. But does this have to be the case?In 1967, Soviet physicist Victor Veselago hypothesized that a material with a negative refractive index could exist without violating any of the laws of physics.Veselago predicted that this remarkable material would exhibit a wide variety of new optical phenomena. However, until recently no one had found such a material and Veselago’s ideas had remained untested. Recently, meta-material samples are being tested for negative refractive index. But the experiments show significant losses and this could be an intrinsic property of negativeindex materials.Snell’s law is satisfied for the materials having a negative refractive index, but the direction of the refracted light ray is ‘mirror-imaged’ about the normal to the surface.There will be an interesting difference in image formation if a vessel is filled with “negative water” having refractive index – 1.33 instead of regular water having refractive index 1.33.Say, there is a fish in a vessel filled with negative water. The position of the fish is such that the observer cannot see it due to normal refraction since the refracted ray does not reach to his eye.But due to negative refraction, he will be able to see it since the refracted ray now reaches his eye.Q. Who hypothesized that a material may have a negative refractive index ?

Read the following text and answer the following questions on the basis of the same:Negative Refractive Index: One of the most fundamental phenomena in optics is refraction. When a beam of light crosses the interface between two different materials, its path is altered depending on the difference in the refractive indices of the materials. The greater the difference, the greater the refraction of the beam. For all known naturally occurring materials the refractive index assumes only positive values. But does this have to be the case?In 1967, Soviet physicist Victor Veselago hypothesized that a material with a negative refractive index could exist without violating any of the laws of physics.Veselago predicted that this remarkable material would exhibit a wide variety of new optical phenomena. However, until recently no one had found such a material and Veselago’s ideas had remained untested. Recently, meta-material samples are being tested for negative refractive index. But the experiments show significant losses and this could be an intrinsic property of negativeindex materials.Snell’s law is satisfied for the materials having a negative refractive index, but the direction of the refracted light ray is ‘mirror-imaged’ about the normal to the surface.There will be an interesting difference in image formation if a vessel is filled with “negative water” having refractive index – 1.33 instead of regular water having refractive index 1.33.Say, there is a fish in a vessel filled with negative water. The position of the fish is such that the observer cannot see it due to normal refraction since the refracted ray does not reach to his eye.But due to negative refraction, he will be able to see it since the refracted ray now reaches his eye.Q. Is Snell’s law applicable for negative refraction ?

When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer?
Question Description
When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer?.
Solutions for When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 12. Download more important topics, notes, lectures and mock test series for Class 12 Exam by signing up for free.
Here you can find the meaning of When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer?, a detailed solution for When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 12 tests.
Explore Courses for Class 12 exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© EduRev
Education Revolution
Follow Us
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup