If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are…
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If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:
- A.
55/601
- B.
601/55
- C.
11/120
- D.
120/11
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Correct answer: C
Let the numbers be a and b.
Given a + b = 55, H.C.F. = 5 and L.C.M. = 120.
Product of the numbers ab = H.C.F. × L.C.M. = 5 × 120 = 600.
Sum of reciprocals = 1/a + 1/b = (a + b)/ab = 55/600 = 11/120.
Key fact used: product of two numbers = H.C.F. × L.C.M.
Algebraic simplification: 1/a + 1/b = (a + b)/ab.