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LCM of two numbers is 495. HCF of these numbers is 5. If the sum of the numbers is 100, find out the difference between the two numbers.
  • a)
    15
  • b)
    12
  • c)
    10
  • d)
    20
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?
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LCM of two numbers is 495. HCF of these numbers is 5. If the sum of th...
It is given that sum of two numbers is 100. Let the two numbers be x and 100 – x and HCF is 5 and LCM is 495
=> We need to apply the formula: HCF x LCM = Product of two numbers
Which gives x(100 – x) = 495 x 5
Solving the equation we get a quadratic which looks like this:

Therefore, Two numbers are 55 and 45
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Most Upvoted Answer
LCM of two numbers is 495. HCF of these numbers is 5. If the sum of th...
Given: LCM = 495, HCF = 5, sum of the numbers = 100

To find: Difference between the two numbers

Solution:

Step 1: Let's assume the two numbers to be x and y

Step 2: We know that LCM * HCF = Product of the numbers i.e., 495 * 5 = x * y

Step 3: Also, we know that x + y = 100

Step 4: Let's find the values of x and y using the above two equations

x * y = 2475 (495 * 5)

x + y = 100

We can solve these equations to get x and y as 45 and 55 respectively.

Step 5: Now, we can find the difference between the two numbers as:

Difference = y - x = 55 - 45 = 10

Therefore, the correct answer is option (c) 10.

Note: We can also solve this question using the formula LCM * HCF = Product of the numbers, and the fact that the sum of the two numbers is equal to the sum of their HCF and LCM. However, the above method is simpler and easier to understand.
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Directions: Read the given passage carefully and answer the question as follow:It is not uncommon for close synonyms to be understood to share the same meaning. The difference between words like “hard” and “difficult”, for example, goes tragically unnoticed. One may employ one or the other with complete indifference, postulating no discrepancy between them. In general, this is well and good; most people lack the scrupulous pedanticalness to quibble over such trifles. Nevertheless, for those of us with ample compulsiveness (and tim e), it is of significant value to comprehend such nuances.Take for example the following sentences: 1) The test was hard. 2) The test was difficult. Is the difference between these synonyms readily apparent? Is there a noticeable difference between them at all? Indeed, these questions are valid and warrant answers. For, what would be the point to having multiple words with the exact same meaning? No, that would be superfluous; the English language being far too economical.While many close synonyms share similar, if not the same, dictionary definitions, the feeling, or mood, they convey is utterly singular. Although a dictionary can provide information about word meanings, pronunciations, etymologies, inflected forms, derived forms, etc., it cannot communicate how it feels to use a word.Granted, the notion that close synonyms can be used interchangeably is prevalent among English speakers. And alas, the dictionary—the text purported to be responsible for clarifying such issues—is of little assistance. In the end, it is left to us, the speakers of the language, those actively responsible for maintaining its sustenance and generation, to understand how these words make us feel and what mood we are inclined to attach to them. Using the examples and insights described above, one may come to recognize these subtle, yet crucial, differences.Q.Which of the following would the author of the passage most likely agreewith?.

Directions: Read the given passage carefully and answer the question as follow:It is not uncommon for close synonyms to be understood to share the same meaning. The difference between words like “hard” and “difficult”, for example, goes tragically unnoticed. One may employ one or the other with complete indifference, postulating no discrepancy between them. In general, this is well and good; most people lack the scrupulous pedanticalness to quibble over such trifles. Nevertheless, for those of us with ample compulsiveness (and tim e), it is of significant value to comprehend such nuances.Take for example the following sentences: 1) The test was hard. 2) The test was difficult. Is the difference between these synonyms readily apparent? Is there a noticeable difference between them at all? Indeed, these questions are valid and warrant answers. For, what would be the point to having multiple words with the exact same meaning? No, that would be superfluous; the English language being far too economical.While many close synonyms share similar, if not the same, dictionary definitions, the feeling, or mood, they convey is utterly singular. Although a dictionary can provide information about word meanings, pronunciations, etymologies, inflected forms, derived forms, etc., it cannot communicate how it feels to use a word.Granted, the notion that close synonyms can be used interchangeably is prevalent among English speakers. And alas, the dictionary—the text purported to be responsible for clarifying such issues—is of little assistance. In the end, it is left to us, the speakers of the language, those actively responsible for maintaining its sustenance and generation, to understand how these words make us feel and what mood we are inclined to attach to them. Using the examples and insights described above, one may come to recognize these subtle, yet crucial, differences.Q.What is the primary purpose of the passage?

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LCM of two numbers is 495. HCF of these numbers is 5. If the sum of the numbers is 100, find out the difference between the two numbers.a)15b)12c)10d)20e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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