Question

The sum of two numbers is 36 and their hcf and lcm are 3 and 105. find the reciprocals of two numbers

Answer 1

hye

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let the 2 numbers be x and y

=>The sum of two numbers is 36

=>x +y = 36

=> hcf and lcm are 3 and 105

so there are 2 possibilites

1)x and y is divisible by 3

2)105 is a mutiple of x and y

if 105 is a mutiple of x and y,then the numbers will be something from this

=> factors of 105 = 1,3,5,7,15,21,35,105

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now here  ,ot of this (1,3,5,7,15,21,35,105) ,
 lets reject the numbers which are not divisible by 3

=> then x and y will be something from this

=>3,15,21,105


now sum should be 36

lets check 1 by 1

=>3 +15 = 17

=>15 + 21 = 36

=>21 +105 = 126


we see that 
=>15 + 21 = 36


∴the 2 numbers are 15 and 21

reciprocal = 1/x = 1/15

=>1/y =1/21

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hope it helps u............

Answer 2

Hi ,

Let a , ( 36 - a ) are two positive numbers.

Their HCF = 3 ,

LCM = 105 ,

we know that ,

LCM × HCF = product of the two numbers

105 × 3 = a ( 36 - a )


315 = 36a - a²


a² - 36a + 315 = 0

a² - 15a - 21a + 315 = 0

a( a - 15 ) - 21 ( a - 15 ) = 0

( a - 15 )(a - 21 ) = 0

a - 15 = 0 or a - 21 = 0

a = 15 or a = 21

Therefore ,

The two numbers are ,

1 ) if a = 15 ,

36 - a = 36 - 15 = 21

2 ) if a = 21

36 - a = 36 - 21 = 15

Therefore ,

Reciprocals of the numbers are

1/15 and 1/21

I hope this helps you.

: )