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

❍ Let the denominator of the fraction be x and according to the given question, the numerator is smaller than the denominator by 7, therefore, the numerator be (x - 7).

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$\underline{\bigstar\;\boldsymbol{According\;to\;the\;Question\;:}}$

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• If one is added to the numerator and one is subtracted from the denominator, then the new fraction is 6/5. Therefore,

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The fraction is,

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• Denominator = (x - 1)
• Numerator = (x - 7 + 1)

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Therefore,

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$:\implies\sf{\dfrac{x-7+1}{x-1}=\dfrac{6}{5}}\\\\\\\\:\implies\sf{\dfrac{x-6}{x-1}=\dfrac{6}{5}}\\\\\\\\:\implies\sf{5(x-6)=6(x-1)}\\\\\\\\:\implies\sf{5x-30=6x-6}\\\\\\\\:\implies\sf{-30+6=6x-5x}\\\\\\\\:\implies\underline{\boxed{\pink{\frak{x=-24}}}}{\;\bigstar}$

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$\therefore\;{\underline{\sf{Hence,\;the\;denominator\;of\;the\;fraction\;is\;{\textsf{\textbf{-24}}}}\;\{Option\;4.\}}}$

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Answer 2

$\large\pmb{\frak{\underline{Answer~:}}}$

• Option 4)
• can't say for sure is correct ✓

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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.

To Find : Find the denominator of the fraction ?

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Solution : Denominator of the fraction be x & Numerator of the fraction be x - 7.

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◗When 1 is added to the numerator and 1 is substracted from the denominator.

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• ${\sf\leadsto{Denominator~=~x - 1}}$
• ${\sf\leadsto{Numerator~=~x - 7 + 1}}$

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◗Finding the denominator of the fraction.

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$\pmb{\sf{\underline{According~ to~ the ~Given ~Question~:}}}$

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$\qquad{\sf:\implies{\dfrac{(x~-~7~+~1)}{(x~-~1)}}}$

$\qquad{\sf:\implies{\dfrac{(x~-~6)}{(x~-~1)}~=~\dfrac{6}{5}}}$

• Cross Multiplication :

$\qquad{\sf:\implies{5(x~-~6)~=~6(x~-~1)}}$

$\qquad{\sf:\implies{5x~-~30~=~6x~-~6}}$

$\qquad{\sf:\implies{6x~-~5x~=~- 30~+~6}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{\pmb{x~=~- 24}}}}}}$★

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Hence,

$\therefore\underline{\sf{The ~denominator ~of ~the ~fraction ~is~\bf{\underline{\pmb{-}\pmb{ 24}}}}}$