Question

The denominator of a rational number is greater than its numerator
4. If the numerator is increased by 1 and the denominator is increas
by 3, the number obtained is . Find the rational number.​

Answer 1

• ³/₇ is the rational number

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$\orange{\bigstar}$  Correct Question  $\green{\bigstar}$

The denominator of a rational number is greater than its numerator by 4. If the numerator is increased by 11 and the denominator is decreased by 1, the new number becomes 7/3. Find the original.

$\orange{\bigstar}$  Given  $\green{\bigstar}$

1 . The denominator of a rational number is greater than its numerator  4

2 .  If the numerator is increased by 11 and the denominator is decreased by 1, the new number becomes 7/3

$\orange{\bigstar}$  To Find  $\green{\bigstar}$

Rational number

$\orange{\bigstar}$  Solution  $\green{\bigstar}$

Let numerator be , " x "

So , Denominator = " x + 4 "

So , Rational number is  $\bf \dfrac{x}{x+4}$

[ ∵ From condition 1 ]

From condition 2 ,

$\to\ \bf \dfrac{x +11}{(x+4)-1}=\dfrac{7}{3}\\\\\to\ \rm 3(x+11)=7(x+4-1)\\\\\to\ \rm 3(x+11)=7(x+3)\\\\\to\ \rm 3x+33=7x+21\\\\\to\ \rm 33-21=7x-3x\\\\\to\ \rm 12=4x\\\\\to\ \rm 4x=12\\\\\to\ \bf x=3\ \; \pink{\bigstar}$

So , Numerator , x = 3

Denominator , x + 4 = 7

So , Rational number = $\bf \dfrac{x}{x+4}=\dfrac{3}{7}$

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