Question

The denominator of a rational number is greater than its numerator by 3. If
numerator and denominator are increased by 1 and 4, respectively, the number
obtained is Find the rational number.
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1
2
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Answer 1

Question:-

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

To Find:-

• Find the rational number.

Solution:-

• Let the numerator be ' x '

• Denominator be ' x + 3 '

According to the Question:-

$\longrightarrow\sf \: \dfrac { x + 1 } { ( x + 3 ) + 4 } = \dfrac { 1 } { 2 }$

$\longrightarrow\sf \: \dfrac { x + 1 } { x + 7 } = \dfrac { 1 } { 2 }$

$\longrightarrow\sf \: 2( x + 1 ) = x + 7$

$\longrightarrow\sf \: 2x + 2 = x + 7$

$\longrightarrow\sf \: 2x - x = 7 - 2$

$\longrightarrow\sf \: x = 5$

Hence ,

• Numerator is 5

• Denominator if x + 3 = 8