Question

The numerator of a rational number is less than its denominator by
3. If numerator is increased by 5 and the denominator is decreased
by 2, the new number becomes 7
6
?

Answer 1

Answer:

let the numerator be x and denominator be y.

given:

x+3 =y ------------(1)

(x+5)/(y-2) = 7/6

6x+30 = 7y -14 -------(2)

substituting 1 in 2,

6x+30 = 7(x+5) -14

6x+30 = 7x + 21 -14

6x+30 = 7x + 7

x = 23 -------(3)

substituting 3 in 1,

y= 23+3 = 26.

Therefore, the rational number is 23/26.

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Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

↝ The numerator of a rational number is less than its denominator by 3.

So, Let we assume that

↝ Numerator of a fraction = x

↝ Denominator of a fraction = x + 3

Thus,

$\red{\rm :\longmapsto\:\boxed{ \rm{ \: Fraction = \frac{x}{x + 3} \: \: }}}$

Further, given that

↝ If numerator is increased by 5 and the denominator is decreased by 2, the new number becomes 7/6.

Now,

↝ Numerator of a fraction = x + 5

↝ Denominator of a fraction = x + 3 - 2 = x + 1

So,

$\red{\rm :\longmapsto\:\boxed{ \rm{ \: Fraction = \frac{x + 5}{x + 1} \: \: }}}$

Now,

$\rm :\longmapsto\:\dfrac{x + 5}{x + 1} = \dfrac{7}{6}$

$\rm :\longmapsto\:7x + 7 = 6x + 30$

$\rm :\longmapsto\:7x - 6x = 30 - 7$

$\bf\implies \:x = 23$

Hence,

$\red{\rm :\longmapsto\:\boxed{ \rm{ \: Fraction = \frac{23}{26} \: \: }}}$