Discussion :: Problems on H.C.F and L.C.M
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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:
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A.
\( \frac { 55 } { 601} \) |
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B.
\(\frac { 601 } { 55 } \) |
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C.
\(\frac { 11 } { 120 } \) |
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D.
\( \frac { 120 } {11 }\) |
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Answer : Option C
Explanation :
Let the numbers be a and b.
Then, a + b = 55 and ab = 5 x 120 = 600.
The required sum =\( \frac { 1 } {a }\)+\( \frac { 1 } { b } \)=\( \frac { a+b } {ab } \)=\(\frac { 55 } { 600 } \)=\( \frac { 11 } { 120 } \)
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