Question

the denominator of a rational number is greater than the numeratorlay 10 . If the numerator is increased by 1 . Denominator is decreased by 1 then the new numberobtainedis 3 / 11 . find the original number
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Answer 1

EXPLANATION.

To find the original number.

Case = 1.

The denominator of a rational number is

greater than the numerator by = 10

Let the numerator of rational number = x

Let the denominator of rational number

=> x + 10

Case = 2.

if the numerator is increased by 1

denominator is decreased by 1

the new number become = 3/11

=> x + 1 / x + 10 - 1 = 3/11

=> x + 1 / x + 9 = 3/11

=> 11 ( x + 1 ) = 3 ( x + 9 )

=> 11x + 11 = 3x + 27

=> 8x = 16

=> x = 2

Therefore,

original fraction = x / x + 10 = 2 / 12 = 1/6

=> original number = 1/6

Answer 2

Answer

²/₁₂ = ¹/₆  $\orange{\bigstar}$

Given

The denominator of a rational number is greater than the numerator by 10 . If the numerator is increased by 1 . Denominator is decreased by 1 then the new numerator obtained is 3 / 11

To Find

Original number

Solution

Let numerator be " x "

So , Denominator is " x + 10 "

A/c , " If the numerator is increased by 1 . Denominator is decreased by 1 then the new numerator obtaine dis 3 / 11 "

$\to \rm \dfrac{x+1}{(x+10)-1}=\dfrac{3}{11}\\\\\to \rm \dfrac{x+1}{x+9}=\dfrac{3}{11}\\\\\to \rm 11(x+1)=3(x+9)\\\\\to \rm 11x+11=3x+27\\\\\to \rm 11x-3x=27-11\\\\\to \rm 8x=16\\\\\to \rm x=2$

So , Numerator , x = 2  $\orange{\bigstar}$

⇒ Denominator , x + 10 = 12  $\orange{\bigstar}$

So , fraction is  $\dfrac{2}{12}\ \orange{\bigstar}$