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:

A. 55/601
B. 601/55
C. 11/120
D. 120/11

• Let the numbers be a and b.
  
  Then, a + b = 55 and ab = 5 x 120 = 600.
  
  The required sum =(1/a)+(1/b)=(a+b)/ab
  =55/600 = 11/120
  
• 9 years agoHelpfull: Yes(40) No(0)
• 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,
  Let numbers are x and 55-x
  x(55-x) = 5*120
  
  solving it , we get numbers as 15 and 40.
  sum of reciprocals = 1/15+1/40 = 11/120 ..... option C
• 12 years agoHelpfull: Yes(13) No(5)
• Simple>
  x*y=Hcf*Lcm
  xy =5*120=600
  We have . x+y=55
  and for reciprocals
  (1/x + 1/y) = (x+y)/xy=55/600=11/120.
  
• 9 years agoHelpfull: Yes(3) No(0)
• a+b=55
  lcm*hcf=a*b=5*12=600
  
  1/a+1/b=a+b/a*b
  55/600=11/120
• 8 years agoHelpfull: Yes(2) No(0)
• Product of numbers= LCM*HCF
  Let the numbers be x and y
  xy=5*120
  xy=600
  and x+y=55
  On solving these equations,we get the value of x and y as 40 and 15
  So,1/40+1/15= 11/120
• 8 years agoHelpfull: Yes(0) No(0)
• Let the numbers be a and b.
  
  Then, a + b = 55 and ab = 5 x 120 = 600.
  
  sum of reciprocol of the two number = 1/a+1/b = a + b/ab=55/600=11/120
  
• 8 years agoHelpfull: Yes(0) No(0)
• A/Q a+b=55,
  a*b=120*5=600;
  and 1/a+1/b= (a+b)/(ab) =55/600 =11/120(ans);
• 8 years agoHelpfull: Yes(0) No(0)
• let the two no. be 5a,5b
  sum=5a+5b=55
  a+b=11
  l.c.m of two numbers(5a,5b)=120
  5(ab)=120
  ab=24
  ((a+b)^2)-((a-b)^2)=4ab
  a-b=5
  a+b=11
  a=8;b=3
  sum of thier reciprocals=1/5a+1/5b
  1/40+1/15=11/120
• 8 years agoHelpfull: Yes(0) No(0)
• product of two numbers = product of HCF and LCM=600
  a+b=55
  a=40,b=15
  1/40+1/15=11/120
• 8 years agoHelpfull: Yes(0) No(0)
• Product of two numbers = LCM*HCF = 5*120
  Sum of reciprocals = sum / product= 55/5*120= 11/20
• 7 years agoHelpfull: Yes(0) No(0)
• answer is C. 11/120
  solution is:-
  1/x + 1/y=x+y/xy
  x+y=55 given
  and xy=5 * 120 ( by using HCF*LCM) formula
  so sun of their reciprocals is 55/600=11/120
• 6 years agoHelpfull: Yes(0) No(0)