the sum of two numbers is 125. their h.c.f and l.c.m are respectively 25 and 150. then the sum of their reciprocals is
Answers
Answer:
Let the numbers be x and y respectively.
According to the question;
x + y =125
y = 125 - x. .....(i),
xy = HCF * LCM
xy = 25 * 150
xy = 3750
put the value of (i) here -
x ( 125 - x ) = 3750
⇒ 125x - x² = 3750
⇒ - x² + 125x - 3750 = 0
⇒ x² - 125x + 3750 = 0
⇒ x² - 75x - 50x + 3750 = 0
⇒ x ( x - 75) - 50 ( x - 75 ) = 0
⇒ ( x - 75 ) ( x - 50 ) = 0
⇒ x = 75 or x = 50
Hence, the two numbers are 75 or 50.
Answer:
let two numbers are x and y respectively.
according to the question x + y = 125 ........( 1 )
and we know that lcm * hcf = product of two numbers
so, x * y = 150 * 25 = 3750 .......( 2 )
from the equation ( 1 ) we get y = 125 - x
now put the value of y in equation ( 2 )
x ( 125 - x ) = 3750
⇒ 125x - x² = 3750
⇒ - x² + 125x - 3750 = 0
⇒ x² - 125x + 3750 = 0
⇒ x² - 75x - 50x + 3750 = 0
⇒ x ( x - 75) - 50 ( x - 75 ) = 0
⇒ ( x - 75 ) ( x - 50 ) = 0
⇒ x = 75 or x = 50
if the value of x = 75 then y = ( 125 - 75 ) = 50
if the value of x = 50 then y = ( 125 - 50 ) = 75
then the two numbers are 75 and 50
reciprocal value of 75 is 1 / 75
reciprocal value of 50 is 1 / 50
sum of these reciprocals are ( 1/75 + 1/ 50 ) = 1/ 30
so the answer is 1/30