Question

If the sum of two numbers is 105 and their H.C.F.
and L.C.M. are respectively 7 and 392, then what
will the sum of the reciprocal of the numbers ?​

Answer 1

Answer:

let the numbers be x and y say

x+y=105

lcm=7

hcf=392

x×y=lcm×hcf

x×y=7×392=2744

1/x+1/y=(y+x)/xy

105/2744

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Answer 2

The Sum Of the Reciprocal Of The Numbers Is

$\frac{15}{392}$

GIVEN

Sum of 2 numbers = 105

HCF of numbers = 7

LCM of the numbers = 392.

TO FIND

The sum of the reciprocal of the numbers.

SOLUTION

We can simply solve the above problem as follows;

Let,

the first number be, a.

The second number is, b.

It is given,

a+ b = 105

LCM = 392

HCF of a and b = 7.

We know that the HCF is the largest number that can divide both numbers.

For example, the HCF of 8 and 12 is 4.

We can also write it as -

4 × 2 = 8

4× 3 = 12.

Similarly,

7 is the common factor between a and b.

Let 'x' be the number that can be multiplied by 7 to give the number 'a'.

So,

7 × x = a.

Let 'y' be the number that can be multiplied by 7 to give the number 'b'.

So,

7 × y = b.

We know that,

the product of numbers = the product of their LCM and HCF.

Therefore,

(7 × x) × (7 × y) = 7 × 392

Simplifying the above equation,

x × y = 56.

Now

We have to find factor pair of 56.

56 × 1 = 56

7 × 8 = 56

2 × 28 = 56

4 × 14 = 56.

if we take 7 as x and 8 as y

we know that,

a + b = 105

We can also write it as-

7 × 7 + 7× 8 = 105

49 + 56 = 105

Hence, the value of a is 49, and the value of b is 56.

We have to calculate the sum of the reciprocal of a and b

Reciprocal of 49 = 1/49

Reciprocal of 56 = 1/56.

So,

$\frac{1}{49} + \frac{1}{56}$

=

$\frac{8 + 7}{392} = \frac{15}{392}$

Hence, the sum of the reciprocal of the numbers is

$\frac{15}{392}$

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