Question

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

Answer 1

Step-by-step explanation:

Let’s assume the two numbers to be X and Y.

X+Y = 27

HCF(X,Y) = 3

LCM(X,Y) = 60

We know that, HCF * LCM = Product of two numbers

3 * 60 = X * Y

XY = 180

1/X + 1/Y = (X+Y)/XY

= 27/180 = 9/60 = 3/20

Answer 2

If the sum of two numbers is 27 and their HCF and LCM are 3 and 60 respectively, then the sum of their reciprocal is 3/20.

Given,

Sum of two numbers = 27

Their HCF = 3

Their LCM = 60

To Find,

Sum of the reciprocal of the numbers = ?

Solution,

Let the numbers be x and y.

Sum of the numbers = 27

⇒ x + y = 27 ----> eq 1

HCF of  x and y = 3

LCM of x and y = 60,

To find the sum of reciprocal of numbers ⇒ $\frac{1}{x} +\frac{1}{y} = ?$

Product of two numbers = Product of HCF and LCM

⇒ xy = HCF of x * LCM of y

⇒ xy = 3 * 60

xy = 180 ----> eq 2

$\frac{1}{x} + \frac{1}{y} \\= \frac{x+y}{xy}$

substituting from eq 1 and eq 2, we get,

= 27/ 180

= 3/20

Therefore, if the sum of two numbers is 27 and their HCF and LCM are 3 and 60 respectively, then the sum of their reciprocal is 3/20.

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