Question

17. A number increased by 20% gives 30. The number is​

Answer 1

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

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Numerator is 4 less than denominator

If 1 is added to both then the fraction becomes 1/2

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

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Required fraction = ??

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

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Let the denominator be x

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Therefore numerator is x - 4

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Acc. to the question :-

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$\sf :\implies\:{\dfrac{x-4+1}{x+1} = \dfrac{1}{2}}$

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$\sf :\implies\:{\dfrac{x- 3}{x+1} = \dfrac{1}{2}}$

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$\sf :\implies\:{2 ( x - 3 ) = x + 1 }$

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$\sf :\implies\:{2x - 6 = x + 1 }$

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$\sf :\implies\:{2x - x = 6 + 1 }$

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$\sf :\implies\:{x = 7 }$

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Putting value of x in the fraction

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Numerator = x - 4 = 7 - 4 = 3

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Denominator = x = 7

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

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Required fraction = 3 / 7

Answer 2

$\huge {\underline{ \underline{ \pink{\bold{required \: answer}}}}}$

let the number be x

20% of x is ;

$\frac{x \times 20}{100} = \frac{20x}{100}$

• original number is x
• after 20% increased it became 30

$\implies \: x + \frac{20x}{100} = 30 \\ \\ \implies \: \frac{100x + 20x}{100} = 30 \\ \\ \implies \: \frac{120x}{100} = 30 \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: x = \frac{30 \times 100}{120} \: \: \: \: \: \: \: \: \\ \\ \implies \: x = \cancel{ \frac{3000}{120}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: \boxed{x = 25 }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

therefore, the number is 25