Question

At a banquet the ratio of the number of boys to the number of girls is 5:3. Halfway through the banquet 20 boys leave and the ratio becomes 5:4. How many girls are at the banquet?​

Answer 1

Answer:

Answer:

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

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Ratio of boys : girls = 5 : 3

Ratio after 20 boys left = 5 : 4

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______________________

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

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No. of girls = ??

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

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let the no. of boys and the no. of girls be 5x and 3x

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Acc. to the question :-

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$\sf :\implies\: {\bold{\dfrac{5x - 20 }{3x } = \dfrac{5}{4}}}$

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$\sf :\implies\: {\bold{( 5x - 20)\times 4 = 5 \times 3x }}$

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$\sf :\implies\: {\bold{ 20x - 80 = 15x}}$

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$\sf :\implies\: {\bold{ 20x = 15 x + 80 }}$

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$\sf :\implies\: {\bold{ 20x - 15x = 80 }}$

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$\sf :\implies\: {\bold{ 5x = 80 }}$

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$\sf :\implies\: {\bold{ x = \dfrac{80}{5} }}$

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$\sf :\implies\: {\bold{ x = 16 }}$

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Putting value of x in the no. of girls

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No. of girls = 3x

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No. of girls = 3 × 16

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No. of girls = 48

______________________

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

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Number of girls in the banquet is 48

Answer 2

Answer:

$Ratio of boys : girls = 5 : 3</p><p></p><p>Ratio after 20 boys left = 5 : 4</p><p></p><p>⠀⠀⠀⠀</p><p></p><p>______________________</p><p></p><p>\sf{\bold{\green{\underline{\underline{To\:Find}}}}}ToFind</p><p></p><p>⠀⠀⠀⠀</p><p></p><p>No. of girls = ??</p><p></p><p>______________________</p><p></p><p>\sf{\bold{\green{\underline{\underline{Solution}}}}}Solution</p><p></p><p>⠀⠀⠀⠀</p><p></p><p>let the no. of boys and the no. of girls be 5x and 3x</p><p></p><p>⠀⠀⠀⠀</p><p></p><p>Acc. to the question :-</p><p></p><p>⠀⠀⠀⠀</p><p></p><p>\sf :\implies\: {\bold{\dfrac{5x - 20 }{3x } = \dfrac{5}{4}}}:⟹3x5x−20=45</p><p></p><p>⠀⠀⠀⠀</p><p></p><p>\sf :\implies\: {\bold{( 5x - 20)\times 4 = 5 \times 3x }}:⟹(5x−20)×4=5×3x</p><p></p><p>⠀⠀⠀⠀</p><p></p><p>\sf :\implies\: {\bold{ 20x - 80 = 15x}}:⟹20x−80=15x</p><p></p><p>⠀⠀⠀⠀</p><p></p><p>\sf :\implies\: {\bold{ 20x = 15 x + 80 }}:⟹20x=15x+80</p><p></p><p>⠀⠀⠀⠀</p><p></p><p>\sf :\implies\: {\bold{ 20x - 15x = 80 }}:⟹20x−15x=80</p><p></p><p>⠀⠀⠀⠀</p><p></p><p>\sf :\implies\: {\bold{ 5x = 80 }}:⟹5x=80</p><p></p><p>⠀⠀⠀⠀</p><p></p><p>\sf :\implies\: {\bold{ x = \dfrac{80}{5} }}:⟹x=580</p><p></p><p>⠀⠀⠀⠀</p><p></p><p>\sf :\implies\: {\bold{ x = 16 }}:⟹x=16</p><p></p><p>⠀⠀⠀⠀</p><p></p><p>Putting value of x in the no. of girls</p><p></p><p>⠀⠀⠀⠀</p><p></p><p>No. of girls = 3x</p><p></p><p>⠀⠀⠀⠀</p><p></p><p>No. of girls = 3 × 16</p><p></p><p>⠀⠀⠀⠀</p><p></p><p>No. of girls = 48</p><p></p><p>______________________</p><p></p><p>\sf{\bold{\green{\underline{\underline{Answer}}}}}Answer</p><p></p><p>⠀⠀</p><p></p><p>Number of girls in the banquet is 48</p><p></p><p>$

Ratio of boys : girls = 5 : 3

Ratio after 20 boys left = 5 : 4

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______________________

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

ToFind

⠀⠀⠀⠀

No. of girls = ??

______________________

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

Solution

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let the no. of boys and the no. of girls be 5x and 3x

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Acc. to the question :-

⠀⠀⠀⠀

\sf :\implies\: {\bold{\dfrac{5x - 20 }{3x } = \dfrac{5}{4}}}:⟹

3x

5x−20

=

4

5

⠀⠀⠀⠀

\sf :\implies\: {\bold{( 5x - 20)\times 4 = 5 \times 3x }}:⟹(5x−20)×4=5×3x

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\sf :\implies\: {\bold{ 20x - 80 = 15x}}:⟹20x−80=15x

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\sf :\implies\: {\bold{ 20x = 15 x + 80 }}:⟹20x=15x+80

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\sf :\implies\: {\bold{ 20x - 15x = 80 }}:⟹20x−15x=80

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\sf :\implies\: {\bold{ 5x = 80 }}:⟹5x=80

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\sf :\implies\: {\bold{ x = \dfrac{80}{5} }}:⟹x=

5

80

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\sf :\implies\: {\bold{ x = 16 }}:⟹x=16

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Putting value of x in the no. of girls

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No. of girls = 3x

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No. of girls = 3 × 16

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No. of girls = 48

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

Answer

⠀⠀

Number of girls in the banquet is 48

Step-by-step explanation:

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