Question

Number is divided in the ratio 7 : 2. if the second part is 34, find the number

Answer 1

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Ratio of 2 numbers = 7 : 2
• second no = 34

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• First number = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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Let the 1sr number be x

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ATQ :-

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$\sf: \implies\: {\bold{ \dfrac{x}{34}= \dfrac{7}{2}}}$

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$\sf: \implies\: {\bold{ x \times 2 = 34\times 7}}$

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$\sf: \implies\: {\bold{ x = \dfrac{ 34\times 7}{2}}}$

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$\sf: \implies\: {\bold{ x = 17\times 7}}$

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$\sf: \implies\: {\bold{ x = 119}}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• 1st number = 119

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$\sf{\orange{\boxed{\huge{\mathsf{ Verification }}}}}$

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$\sf: \implies\: {\bold{ \dfrac{119}{34}= \dfrac{7}{2}}}$

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$\sf: \implies\: {\bold{ \dfrac{119\div 17}{34\div 17}= \dfrac{7}{2}}}$

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$\sf: \implies\: {\bold{ \dfrac{7}{2}= \dfrac{7}{2}}}$

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⠀⠀⠀⠀⠀⠀⠀⠀.......Hence Verified

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Answer 2

$\sf{\boxed{\boxed{\large{\red{\mathbb{ANSWER}}}}}}$

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Required number is 119

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$\sf{\boxed{\boxed{\large{\red{\mathbb{STEP\: BY\: STEP\: EXPLANATION }}}}}}$

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• Let the required number be a

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ATQ:-

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first number : second number = 7 : 2

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a : 34 = 7 : 2

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• Now we will turn ratio into fractions

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$\sf: \longrightarrow\: {\bold{ \dfrac{a}{34} =\dfrac{7}{2}}}$

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$\sf: \longrightarrow\: {\bold{ a =\dfrac{7\times 34 }{2}}}$

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$\sf: \longrightarrow\: {\bold{ a = {7\times 17}}}$

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$\sf: \longrightarrow\: {\bold{ a = 119 }}$

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