Question

The sum of two numbers is 24 and their
product is 120. What is the sum of their
reciprocals ?

Answer 1

Given :

• sum of two numbers = 24
• product of two numbers = 120

To Find :

• sum of reciprocals of two numbers ?

Solution :

let two numbers are x and y

and it is given that

• sum of numbers = 24
• product of numbers = 130

so,

• x + y = 24 .......(i)
• xy = 130 .........(ii)

now, we have to find sum of their reciprocals

$\bold{reciprocal \: of \: x = \frac{1}{x} } \\ \\ \bold{reciprocal \: of \: y = \frac{1}{y} }$

$\bold{sum \: of \: reciprocals = \frac{1}{x} + \frac{1}{y } } \\ \\ \bold{: \implies \: \frac{x + y}{xy} } \\ \\ \bold{: \implies \: \frac{x + y}{xy} }$

now, put the value of x + y and xy from (i) and (ii)

$\bold{: \implies \: \cancel \frac{24}{130} } \\ \\ \bold{: \implies \: \frac{12}{65} } \: \: \:$

so, sum of reciprocals of numbers is 12/65 or 0.184

Answer 2

$\\ \\ \bf \underline \red{Given : }$

• The sum of two numbers is 24 and their product is 120. What is the sum of their reciprocals ?

$\\ \bf\underline \red {To \: find}$

• Sum of their reciprocals.

$\bf \red{Solution - : }$

$\\ \bf \frac{24}{120} = 0.2$

In fraction form,

$\\ \bf \: 0.2 = \frac{1}{5}$

We already have the sum and the product of the digits. But we don't know the real numbers.The sum of the reciprocals is the sum of the numbers over their product.

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