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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let a and b are two numbers ,
a/c to question,
a + b =55 -------(1)
we know,
HCF( a ,b) × LCM (a , b) = ab
5 × 120 =ab
ab = 600 ---------(2)
divide equation (1) ÷ (2)
(a + b)/ab =55/600
1/b + 1/a =11/120
1/a + 1/b =11/120
a/c to question,
a + b =55 -------(1)
we know,
HCF( a ,b) × LCM (a , b) = ab
5 × 120 =ab
ab = 600 ---------(2)
divide equation (1) ÷ (2)
(a + b)/ab =55/600
1/b + 1/a =11/120
1/a + 1/b =11/120
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