Question

Q.3 plz help friend..,.!!!!!

Answer 1

Given:

• Difference of two natural numbers  is 3
• Difference of reciprocal of numbers is 3/28

To Find:

• Two natural numbers following above conditions

Solution:

Let the two natural numbers be x and y, where x>y

According to the question,

⟼ x-y=3

⟼ x=y+3--------------------(1)

Now,

Reciprocal of first number= $\sf{\dfrac{1}{x}}$

Reciprocal of second number= $\sf{\dfrac{1}{y}}$

We know that for the natural numbers,

Reciprocal of larger number is always less than reciprocal of smaller number

So,

$\longrightarrow\sf{\dfrac{1}{y}-\dfrac{1}{x}=\dfrac{3}{28}}$

From (1)

$\longrightarrow\sf{\dfrac{1}{y}-\dfrac{1}{y+3}=\dfrac{3}{28}}$

$\longrightarrow\sf{\dfrac{y+3-y}{y}=\dfrac{3}{28}}$

$\longrightarrow\sf{\dfrac{\cancel{3}}{y}=\dfrac{\cancel{3}}{28}}$

$\longrightarrow\sf{\dfrac{1}{y}=\dfrac{1}{28}}$

$\longrightarrow\sf{y=28}$

On putting value of y in (1), we get

➳ x= 28+3

➳ x= 31

Hence, the required natural numbers are 31 and 28.