Question

The numerator of a rational number is greater than its denominator by 6. if the numerator and denominator and increasing by 7 and 1 respectively, the number obtained is 5/2. find the rational number

give step by step explanation​

Answer 1

Answer:

Let the numerator of the rational number be x.

Then, the denominator of the rational number =x+6.

It is given that the numerator is increased by 5 and the denominator is decreased by 3.

∴ the numerator of the new rational number =x+5.

Denominator of the new rational number =(x+6)−3=x+3

∴ new rational number =

x+3

x+5

But the new rational number is given as

4

5

.

∴

x+3

x+5

=

4

5

By cross multiplying, we get,

4(x+5)=5(x+3)

⇒4x+20=5x+15

⇒4x−5x=15−20 ....[Transposing 5x to LHS. and 20 to RHS]

⇒−x=−5 or x=5

∴ numerator of the rational number is 5 and denominator = 5+6 i.e. 11.

∴ the required rational number is

11

5

.

Answer 2

Given : The numerator of a rational number is greater than its denominator by 6 & if the numerator and denominator and increasing by 7 and 1 respectively, the number obtained is 5/2.

To Find : Find the rational numbers ?

_________________________

Solution : Let the other number be a.

$~$

Therefore,

• Positive number
• A positive number is 5 times other number

$~$

$\qquad{\sf:\implies{Postive~ number~=~5~×~Other~number}}$

$\qquad{\sf:\implies{Postive~ number~=~5~×~a}}$

$\qquad:\implies{\underline{\boxed{\frak{\purple{\pmb{Postive~ number~=~5a}}}}}}$★

$~$

$\pmb{\sf{\underline{According~ to~ the ~Given ~Question~:}}}$

$~$

◗If 21 is added to both the numbers, then one of the new numbers become twice of other new numbers.

$~$

$\qquad{\sf:\implies{21~+~ Positive ~number~=~2(Other~number~+~21)}}$

$\qquad{\sf:\implies{21~+~5a~=~2(a~+~21)}}$

$\qquad{\sf:\implies{21~+~5a~=~2a~+~42}}$

$\qquad{\sf:\implies{5a~=~2a~+~42~-~21}}$

$\qquad{\sf:\implies{5a~=~2a~+~21}}$

$\qquad{\sf:\implies{5a~-~2a~=~21}}$

$\qquad{\sf:\implies{3a~=~21}}$

$\qquad{\sf:\implies{a~=~\cancel\dfrac{21}{7}}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{\pmb{a~=~7}}}}}}$★

$~$

Here,

• a denotes Other number which is 7 and The Positive number is 5a = 5 × 7 = 35.

$~$

Hence,

$\therefore\underline{\sf{The~ rational ~numbers~ are~\bf{\underline{\pmb{7}}}~\sf{\&}~\bf{\underline{\pmb{35}}}}}$