Question

If the sum of two numbers is 27 and their hcf and lcm are 3 and 60 then sum of their reciprocal is

Answer 1

Let the no. be a and b
• a + b = 27 
a = 27 - b .....( i )
Since , 
HCF × LCM = product of two nos.
3 × 60 = ab
180 = ab .....( ii )
Putting in ( ii ) value of a from ( i )
ab = 180
( 27 - b ) b = 180
27b - b² = 180
b² - 27b + 180 = 0
b² - 12b - 15b + 180 = 0
b ( b - 12 ) - 15 ( b - 15 ) = 0
( b - 12 ) ( b - 15 ) = 0

• ( b - 12 ) = 0b = 12

• ( b - 15 ) = 0b = 15
If we take b = 12
a = 27 - b
a = 27 - 12
a = 15


If we take b = 15
a = 27 - b
a = 12