Question

The denometer of rational number is greater than the numerator 4.if the numerator by decrease by 5and demorator decrese by 2 . The number obtained is 4/5 .what is rational number.

Answer 1

Answer

• These rational number be (x/y) = 33/37

Step - by - Step - Explanation

Given:-

• The denominator of rational number is greater than the numerator 4.
• the numerator decrease by 5 and denominator decrease by 2 , The number obtained is 4/5

Find :-

• These Rational Number

Now, Going To Explanation ,

Let,

• Numerator be = x
• Denominator be = y

A /C to question,

(The denominator of rational number is greater than the numerator 4)

➡ y = x + 4

➡x - y = -4 _____________(1)

Again,

(the numerator decrease by 5 and denominator decrease by 2 , The number obtained is 4/5)

➡(x-5)/(y-2) = 4/5

➡ 5 × (x-5) = 4 × (y-2)

➡5x - 4y = -8 + 25

➡5x - 4y = 17 ____________(2)

Multiply by 5 in equ(1)

➡5x - 5y = -20 ___________(3)

Subtract equ(2) & equ(3)

➡-4y + 5y = 17 + 20

➡y = 37

Keep value of (y=36) in equ(2)

➡5x - 4×37 = 17

➡5x = 17 + 148

➡5x = 165

➡x = 165/5

➡x = 33

_______________

Answer 2

$\huge\bold{\underbrace{\red{SOLUTION:-}}}$

GIVEN :-

• The denominator of a rational number is greater than the numerator by 4 .

• If the numerator is decreased by 5 and the denominator is decreased by 2, then the number obtained is 4/5 .

TO FIND :-

• The original rational number .

CALCULATION :-

Let,

✍️ The numerator of the rational number be “x” .

✍️ And the denominator be “y” .

Hence, the original rational number is

• $\rm{\red{\dfrac{x}{y}}}$

According to the question,

• y = x + 4 ------(1)

✍️ If the numerator is decreased by 5, then the numerator is,

• x - 5 .

✍️ And if the denominator is decreased by 2, then the denominator is,

• y - 2 .

Again, according to the question

• $\rm{\red{\dfrac{x\:-\:5}{y\:-\:2}\:=\:\dfrac{4}{5}\:}}$

$<font color=green>$

$\rm{\implies\:5\:(x\:-\:5)\:=\:4\:(y\:-\:2)\:}$

$\rm{\implies\:5x\:-\:25\:=\:4y\:-\:8\:}$

$\rm{\implies\:5x\:-\:4y\:=\:25\:-\:8\:}$

$\rm{\implies\:5x\:-\:4y\:=\:17\:}$

✍️ Putting the value of ‘y = x + 4’,

$\rm{\implies\:5x\:-\:4\:(x\:+\:4)\:=\:17\:}$

$\rm{\implies\:5x\:-\:4x\:-\:16\:=\:17\:}$

$\rm{\implies\:x\:=\:17\:+\:16\:}$

$\rm\blue{\implies\:x\:=\:33\:}$

✍️ Now, putting the value of “x = 33” in the equation [1]

$\rm{\implies\:y\:=\:33\:+\:4\:}$

$\rm\blue{\implies\:y\:=\:37\:}$

$\pink\bigstar\:\rm{\purple{\boxed{\blue{\therefore\:\dfrac{x}{y}\:=\:\dfrac{33}{37}\:}}}}$