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Maths-

General

Easy

Question

In a rational number, the denominator exceeds the numerator by 4. If the numerator and denominator are both increased by 9, the rational number becomes $7 over 8$ Find the original rational number

hint Hint:

Frame the equation according to the information provided and then get the
original rational number.

The correct answer is: 19/23

Given, the denominator is 4 more than its numerator.
Let the numerator of rational number = x
And denominator be x + 4
So, original rational number = $fraction numerator x over denominator x plus 4 end fraction$
Given that if numerator and denominator increased by 9, then the rational number
becomes $7 over 8$ .
$not stretchy rightwards double arrow fraction numerator x plus 9 over denominator x plus 4 plus 9 end fraction equals 7 over 8$
$not stretchy rightwards double arrow fraction numerator x plus 9 over denominator x plus 13 end fraction equals 7 over 8$
By cross multiplication, we get $8 left parenthesis x plus 9 right parenthesis equals 7 left parenthesis x plus 13 right parenthesis$
$not stretchy rightwards double arrow 8 x plus 72 equals 7 x plus 91$
$not stretchy rightwards double arrow 8 x minus 7 x equals 91 minus 72$
$not stretchy rightwards double arrow x equals 19$
So, numerator $x equals 19$
and denominator x + 4 = 19 + 4 = 23
Hence the original rational number = $fraction numerator x over denominator x plus 4 end fraction equals 19 over 23$

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