Ques. 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 the two numbers be X and Y
given X+Y=55
we know that
HCF × LCM = product of the two numbers
so
5×120=X×Y
X×Y=600
Now,
1/X+1/Y
=(X+Y) / X×Y
=55/600
or 11/120
hence your answer is 55/600 or 11/120
given X+Y=55
we know that
HCF × LCM = product of the two numbers
so
5×120=X×Y
X×Y=600
Now,
1/X+1/Y
=(X+Y) / X×Y
=55/600
or 11/120
hence your answer is 55/600 or 11/120
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