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HCF and LCM of two numbers is 8 and 96. Sum of those numbers is 56. Then what is sum of their reciprocals?
  • a)
    1/56
  • b)
    7/96
  • c)
    1/96
  • d)
    1/8
  • e)
    8/56
Correct answer is option 'B'. Can you explain this answer?
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HCF and LCM of two numbers is 8 and 96. Sum of those numbers is 56. Th...
Given:
HCF = 8
LCM = 96
Sum of numbers = 56

To find:
Sum of reciprocals of the numbers

Solution:

Let the two numbers be a and b.
We know that HCF × LCM = a × b
=> 8 × 96 = a × b
=> ab = 768

Also, we know that a + b = 56

We need to find (1/a) + (1/b)
=> (a+b)/ab

Substituting the values we get,
=> (56)/(ab)
=> (56)/(768)
=> 7/96

Therefore, sum of reciprocals of the numbers = 7/96
Hence, option B is the correct answer.
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HCF and LCM of two numbers is 8 and 96. Sum of those numbers is 56. Then what is sum of their reciprocals?a)1/56b)7/96c)1/96d)1/8e)8/56Correct answer is option 'B'. Can you explain this answer?
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