Question

*The numerator of a fraction is smaller than the denominator by 7. If 1 is added to the numerator and 1 is subtracted from the denominator then the new fraction is 6/5. Find denominator of the fraction.*

1️⃣ 11
2️⃣ 16
3️⃣ 9
4️⃣ can't say for sure​

Answer 1

$\large\bf\pink{\mid{\overline{\underline{Correct\:Question }}}\mid}$

The numerator of a fraction is greater than denominator by 7. If 1 is added to numerator and 1 is subtract from Denominator the fraction is 6/5. Find the fraction.

$\sf{\huge{\underline{\green{Given :-}}}}$

• The numerator of a fraction is smaller than the denominator by 7.

• 1 is added to the numerator and 1 is subtracted from the denominator then the new fraction is 6/5.

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The denominator of the fraction.

$\sf{\huge{\underline{\green{Answer :-}}}}$

According to the question,

The numerator of a fraction is smaller than the denominator by 7.

Let the denominator be x,

The numerator be ( x + 7 )

The fraction obtained = $\dfrac{(x + 7)}{x}$

1 is added to the numerator and 1 is subtracted from the denominator then the new fraction is 6/5.

➝ $\dfrac{(x + 7) + 1}{x - 1} = \dfrac{6}{5}$

➝ $\dfrac{x + 7 + 1}{x - 1} = \dfrac{6}{5}$

➝ $\dfrac{x + 8 }{x - 1} = \dfrac{6}{5}$

➝ 5 ( x + 8 ) = 6 ( x - 1 )

➝ 5x + 40 = 6x - 6

➝ 5x - 6x = - 6 - 40

➝ - x = - 46

➝ x = 46

We have the fraction ,

Numerator = x + 7 = 46 +7 = 53

➝ $\dfrac{(53)}{46}$

The denominator of the fraction is - 46 .

$\sf{\huge{\underline{\green{Answer :-}}}}$

$\dfrac{(x + 7) + 1}{x - 1} = \dfrac{6}{5}$

➝ $\dfrac{(46 + 7) + 1}{46 - 1} = \dfrac{6}{5}$

➝ $\dfrac{(53) + 1}{46 - 1} = \dfrac{6}{5}$

➝ $\dfrac{54}{45} = \dfrac{6}{5}$

➝ $\dfrac{6}{5} = \dfrac{6}{5}$

LHS = RHS