Question

the numerator of a fraction is 3 less than its denominator if the denominator is increased by 2 and the numerator is decreased by 5 the fraction becomes 28 by 33find the original farction​

Answer 1

Answer:

For the original fraction ,

let its numerator be x and denominator be (x+3)

∴ the fraction is x/(x+3)

After doing the changes we get

ATP,

       ( x - 5 ) / ( x + 3 + 2) = 28 / 33

   ⇒ ( x - 5 ) / ( x + 5 ) = 28 / 33

   ⇒ 33x - 165 = 28x + 140

   ⇒ 5x = 305

   ⇒ x = 61

∴ The fraction = x / (x+3) = 61/64

Hope this helps u :-)

Answer 2

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

Required fraction is 61/64

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

Given :- Numerator of a fraction = 3 less than denominator of a fraction

If denominator is increased by 2 and numerator is decreased by 5 the resultant fraction will be 28/33

To find :- Required fraction

Solution :-

Let the denominator of the fraction be x

Numerator of a fraction = 3 less than denominator of a fraction = 3 less than x = x - 3

When denominator is increased by 2 = x + 2

When numerator is decreased by 5 = (x - 3) - 5

And also If denominator is increased by 2 and numerator is decreased by 5 the resultant fraction will be 28/33

According to the question :-

We can form an equation

Equation formed :-

$\boxed{ \sf \dfrac{(x - 3) - 5}{x + 2} = \dfrac{28}{33} }$

$\sf \dfrac{x - 3 - 5}{x + 2} = \dfrac{28}{33}$

$\sf \dfrac{x - 8}{x + 2} = \dfrac{28}{33}$

By cross multiplication :-

$\sf (x - 8)33 = 28(x + 2)$

$\sf 33x - 264 = 28x + 56$

$\sf 33x - 28x - 264 = 56$

$\sf 5x - 264 = 56$

$\sf 5x = 56 + 264$

$\sf 5x = 320$

$\sf x = \dfrac{320}{5}$

$\sf x = 64$

Denominator of the required fraction = x = 64

Numerator of required fraction = x - 3 = 64 - 3 = 61

So required fraction = 61/64

$\mathfrak{\large{\underline{\underline{Verification:-}}}}$

Let us check

$\sf \dfrac{(61) - 5}{64 + 2} = \dfrac{28}{33}$

$\sf \dfrac{61 - 5}{66} = \dfrac{28}{33}$

$\sf \dfrac{56}{66} = \dfrac{28}{33}$

$\sf \dfrac{56 \div 2}{66 \div 2} = \dfrac{28}{33}$

$\sf \dfrac{28}{33} = \dfrac{28}{33}$