Question

the denominator of a number is greater than it numerator by 7 if numerator is increased by 19 and denominator decreased by 3 the new number becomes 4 find original one​

Answer 1

EXPLANATION.

• GIVEN

Denominator of a number is greater than it's

numerator by 7.

if numerator is increased by 19 and denominator

decreased by 3 the new number = 4

To find the original number.

According to the question,

Let the numerator of a rational number = x

Let the denominator of a rational number

= x + 7

if numerator is increased by = 19

=> x + 19

denominator decreased by = 3

=> x + 7 - 3 => x + 4

New rational number = x + 19 / x + 4

new number = 4

Therefore,

=> x + 19 / x + 4 = 4

=> x + 19 = 4( x + 4 )

=> x + 19 = 4x + 16

=> 19 - 16 = 4x - x

=> 3 = 3x

=> x = 1

Numerator of a rational number = 1

Denominator of a rational number =

=> x + 7 = 8

Therefore,

New rational number = 1/8

Answer 2

$\large\bf{\underline{\underline{\red{SOLUTION:-}}}}$

GIVEN :-

• The denominator of a number is greater than its numerator by 7 .
• If numerator is increased by 19 and denominator by 3 , then the new number becomes 4 .

To Find :-

• The Original number .

SOLUTION :-

️ Let,

• The numerator be “x”
• So, the denominator be “(x + 7)” .

✴️ According to question,

• Numerator is increased by “19” and denominator is decreased by “3” .

▼ So now ,

• Numerator is “x + 19”
• Denominator is “x + 19 - 7” = “x + 4” .

✴️ New rational number is,

• $\rm{\pink{\boxed{\dfrac{x\:+\:19}{x\:+\:4}}}}$

✴️ Again, Given that the New number becomes “4” .

$\rm{\implies\:\dfrac{x\:+\:19}{x\:+\:4}\:=\:4\:}$

$\rm{\implies\:(x\:+\:19)\:=\:4(x\:+\:4)\:}$

$\rm{\implies\:x\:=\:1\:}$

️ Therefore,

• Numerator of the numerical number is “1” .
• Denominator of the numerical number is “x + 7” = “8” .

$\bigstar\:\bf{\underline{\blue{\boxed{Original\:number\:is\:\:\dfrac{1}{8}\:}}}}$