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If the sum of two numbers is 66 and the H.C.F and L.C.M of the numbers are 6 and 120 respectively, then the sum of the reciprocals of numbers is equal to∶

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If the sum of two numbers is 66 and the H.C.F and L.C.M of the numbers are 6 and 120 respectively, then the sum of the reciprocals of numbers is equal to∶
1). 11/120
2). 21/120
3). 15/130
4). 55/120

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1 answers

0 vote
Answered by on | Votes 0 |

Let the numbers are x and y

Then, x + y = 66

We know that,

LCM × HCF = Product of two numbers

⇒ xy = 6 × 120 = 720

∴ required sum $(= \frac{1}{{\rm{x}}} + \frac{1}{{\rm{y}}} = \frac{{\left( {{\rm{x\;}} + {\rm{\;y}}} \right)}}{{{\rm{xy}}}} = \frac{{66}}{{720}} = \frac{{11}}{{120}})$

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