The sum of two numbers is 36 and their H.C.F and L.C.M. are 3 and 105 respectively. The sum of the reciprocals of the two numbers will be:
13
$\dfrac {9}{11}$
$\dfrac {7}{35}$
$\dfrac {4}{35}$
Solution
sum = 36 = 3 × 12
HCF = 3
LCM = 105
LCM/GCD = 105/3 = 35
35 = 1 × 35
= 5 × 7
No. 1 = HCF × uncommon factor 1
and No. 2 = HCF × uncommon factor 2
so pair of numbers is = 1 × 3 and 35 × 3
= 3 and 105 but sum is not 36
another pair 3 × 5 and 3 × 7
pair is 15 and 21 sum = 36
sum of reciproclas
= 1/15 + 1/21
= (7 + 5)/105
= 12/105=4/35