Question

the denominator of a fraction is greater than the numerator by 8 if the numerator is increased by 17 and denominator is decreased by 1 the number of 10 is 3 by 2 find the fraction​

Answer 1

$\large\underline\mathrm\red{CORRECT \:QUESTION:-}$

The denominator of a fraction is greater than the numerator by 8 if the numerator is increased by 17 and denominator is decreased by 1, then the fraction becomes3 by 2 find the fraction.

$\huge\underline\mathrm\red{GIVEN:-}$

• The denominator of a fraction is greater than the numerator by 8
• The numerator is increased by 17 and denominator is decreased by 1

$\huge\underline\mathrm\red{TO\:FIND:-}$

Find the fraction = ?

$\huge\underline\mathrm\red{SOLUTION:-}$

Let the numerator and denominator of the fraction be x and y respectively.

Then,

• $\large\rm{<strong> </strong><strong>Fraction</strong><strong> </strong><strong>=</strong><strong> </strong>}$$\large{\bf {\frac{x}{y}}}$

It is given that

$\bf{<em> </em><em>Denominator</em><em> </em><em>=</em><em> </em><em>N</em><em>u</em><em>m</em><em>e</em><em>r</em><em>a</em><em>t</em><em>o</em><em>r</em><em> </em><em>+</em><em> </em><em>8</em><em> </em>}$

$\implies$$\bf\blue{ y = x + 8...1)}$

• if the numerator is increased by 17

New numerator = (x + 17)

• If the denominator is decreased by 1

New Denominator = (y - 1)

According to given conditions, we have

$\implies$$\large{\bf {\frac{(x+17)}{(y-1)}}}$ = $\large{\bf {\frac{3}{2}}}$

Using cross product, we get

$\implies$$\bf{2(x + 17) = 3(y-1)}$

$\implies$$\bf{2x + 34 = 3y - 3}$

$\implies$$\bf{34 + 3 = 3y - 2x}$

$\implies$$\bf\blue{37 = 3y - 2x...2)}$

Put the value of y from equation 1) in equation 2)

$\implies$$\bf{37 = 3(x + 8) - 2x}$

$\implies$$\bf{37 = 3x + 24 - 2x}$

$\implies$$\bf{37 - 24 = x}$

$\large{\boxed{\bf{\green{x = 13}}}}$

Put the value of x in equation 1)

$\implies$$\bf{y = 13 + 8}$

$\large{\boxed{\bf{\green{y = 21 }}}}$

Then, the fraction becomes $\large{\bf {\frac{13}{21}}}$

$\large\underline\mathrm\red{FINAL \:ANSWER:-}$

$\huge{\boxed{\bf{\green{Fraction = \frac{13}{21} }}}}$

Answer 2

Answer:

$\implies$ The fraction = 13/21.

$\large\underline\mathrm{Given:-}$

• The denominator of a fraction is greater than the numerator by 8.
• The numerator is increased by 17 and denominator is decreased by 1.

$\large\underline\mathrm{To \: find}$

The fraction x/y = ?

$\implies$ Dominator = Numerator + 8

$\implies$ y = x + 8. .....(1)

• The numerator is increased by 17

$\implies$ Numerator = (x + 17)

• The Denominator is decreased by 1

$\implies$ Denominator = (y - 1)

We have,

$\implies$ (x + 17)/(y - 1) = 3/2

Using the cross multiple.

$\implies$ 2(x + 17) = 3(y - 1)

$\implies$ 2x + 34 = 3y - 3

$\implies$ 34 + 3 = 3y - 2x

$\implies$ 37 = 3y - 2x. ....(2)

The value of y from Eq (1)

$\implies$ 37 = 3(x + 8) - 2x

$\implies$ 37 = 3x + 24 - 2x

$\implies$ 37 - 24 = x

$\implies$ x = 13

Put the value of x.

$\implies$ y = 13 + 8

$\implies$ y = 21

Then,

The fraction = 13/21.