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in a school the number of girls exceeds number of boys by 15%.Find the ratio of the number of boys to girls​

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Starrysoul100idn

[tex]\bold{\huge{\green{\underline{ Solution }}}}[/tex]

[tex]\bold{\underline{ Given :- }}[/tex]

  • In a school, the number of girls are 15% more than boys

[tex]\bold{\underline{ To\: Find :- }}[/tex]

  • We have to find the ratio of the number of boys to the girls

[tex]\bold{\underline{ Let's \: Begin :- }}[/tex]

Let the total strength of the class be 100 and number of girls be x

Therefore,

The number of boys be = x - 15

According to the question,

[tex]\sf{ Total \:strength = x + ( x + 15 )}[/tex]

[tex]\sf{ 100 = 2x + 15}[/tex]

[tex]\sf{ 100 - 15 = 2x }[/tex]

[tex]\sf{ 85 = 2x }[/tex]

[tex]\sf{x = 85/2}[/tex]

Thus, The number of girls be 85/2

Now,

Number of boys = 85/2 - 15

[tex]\sf{boys = 85 - 30/2 }[/tex]

[tex]\sf{ boys = 55/2 }[/tex]

Ratio of boys and girls :-

[tex]\sf{ = 55/2/85/2}[/tex]

[tex]\sf{= 55/85}[/tex]

[tex]\sf{= 11/17 }[/tex]

Hence, The ratio of the girls and boys is 11:17 .

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