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 two numbers be x and y
then atq
x+y=55
x=55-y - - - - - - - - - - 1
now
HCF×LCM= x×y
5×120=xy
600= 55y -y²
y² -55y+600
y² - 40y-15y +600
y(y-40)-15(y-40)
therefor
y=40 or y=15
now
numbers came to be 15 and 40
1/15+1/40=11/120----------------------------------------------ans
then atq
x+y=55
x=55-y - - - - - - - - - - 1
now
HCF×LCM= x×y
5×120=xy
600= 55y -y²
y² -55y+600
y² - 40y-15y +600
y(y-40)-15(y-40)
therefor
y=40 or y=15
now
numbers came to be 15 and 40
1/15+1/40=11/120----------------------------------------------ans
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