Question

solve this . . . . . . . . . . . ​

Answer 1

Solution :

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

Two number difference is 5 and there opposite number difference is 1/10.

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

The number .

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

Let the one number be r

Let the other number be m

A/q

$\longrightarrow\sf{r-m=5....................(1)}$

&

$\longrightarrow\sf{\dfrac{1}{m} -\dfrac{1}{r}=\dfrac{1}{10} }\\\\\\\longrightarrow\sf{\dfrac{r-m}{rm} =\dfrac{1}{10} }\\\\\\\longrightarrow\sf{10(r-m)=rm}\\\\\\\longrightarrow\sf{10(5)=rm\:\:[from(1)]}\\\\\\\longrightarrow\sf{50=rm}\\\\\\\longrightarrow\sf{r=\dfrac{50}{m} ..............(2)}$

Putting the value of r in equation (1),we get;

$\longrightarrow\sf{\dfrac{50}{m} -m=5}\\\\\\\longrightarrow\sf{50-m^{2} =5m}\\\\\\\longrightarrow\sf{m^{2} -5m-50=0}\\\\\\\longrightarrow\sf{m^{2} +10m-5m-50=0}\\\\\\\longrightarrow\sf{m(m+10)-5(m+10)=0}\\\\\\\longrightarrow\sf{(m+10)(m-5)=0}\\\\\\\longrightarrow\sf{m+10=0\:\:\:Or\:\:\:m-5=0}\\\\\\\longrightarrow\sf{\pink{m\neq -10\:\:\:Or\:\:\:m=5}}$

Putting the value of m in equation (2),we get;

$\longrightarrow\sf{r=\cancel{\dfrac{50}{5} }}\\\\\\\longrightarrow\sf{\pink{r=10}}$

Thus;

$\underbrace{\bf{The\:number\:is\:r=10\:\& \:m=5}}}}}$

Answer 2

QueStI0N -

The difference between two numbers is 5 and the difference between the reciprocal of the two numbers is 10 .

Then, find the numbers .

S0LUTI0N -

Let the given numbers be x and y respectively .

In the above Question , we have the following information given -

The difference between two numbers is 5 and the difference between the reciprocal of the two numbers is 10 .

So, We can use this to form the following equations -

x - y = 5 ........ ( 1 )

( 1 / x ) + ( 1 / y ) = 10

=> (x + y ) / xy = 10 . ...... ( 2 )

From equation 1,

x - y = 5

=> x = 5 + y

Substuting this value in the second Equation -

(x - y ) / xy = 10

=> Substitute x = y + 5

=> y^2 - 5y - 50 = 0

=> y^2 - 10y + 5y - 50 = 0

=> y ( y - 10 ) + 5 ( y - 10 ) = 0

=> (y - 10 )( y + 5 ) = 0

Hence, the value of y can be either 10 or -5

But y = -5 is not possible .

Now ,.

If y = 10, x = 5

Hence , the required numbers are 5 and 10 respectively ...