Math, asked by sishilgupta777777, 28 days ago

in class 10th of a school the ratio of the number of boys to that of the girls is 4:3 if there were 20 more boys and 12 less girls then the ratio would have been 2:1 how many students were there in the class​

Answers

Answered by mddilshad11ab
145

\sf\small\underline\purple{Let:-}

\tt{\implies Number\:of\:boys=4x}

\tt{\implies Number\:of\: girL=3x}

\sf\small\underline\purple{Given:-}

\tt{\implies Ratio\:of\:boys\:to\:girls=4:3}

\sf\small\underline\purple{To\: Find:-}

\sf{\implies Number\:of\: students=?}

\sf\small\underline\purple{Solution:-}

To calculate the number of students in class at first we have to set up equation then solve to find out the value of x.

\sf{\implies \dfrac{boys+20}{girls-12}=\dfrac{2}{1}}

\rm{\implies \dfrac{4x+20}{3x-12}=\dfrac{2}{1}}

\tt{\implies 4x+20=6x-24}

\tt{\implies 4x-6x=-24-20}

\tt{\implies -2x=-44}

\tt{\implies 2x=44}

\tt{\implies x=22}

  • Now calculate the no of boys and girls

\tt{\implies Number\:of\:boys=4x}

\tt{\implies 4\times\:22}

\tt{\implies 88\:boys}

\tt{\implies Number\:of\:girL=3x}

\tt{\implies 3\times\:22}

\tt{\implies 66\:girL}

  • Now calculate total students

\tt{\implies Total\:_{(student)}=Total\:_{(boys)}+Total\:_{(girL)}}

\tt{\implies Total\:_{(students)}=88+66}

\tt{\implies Total\:_{(students)}=154}

\sf\large{Hence,}

\bf{\implies Total\: number\:_{(students)}=154}

Answered by SavageBlast
105

Given:-

  • The ratio of the number of boys to that of the girls is 4:3 in class 10th of a school.

  • If there were 20 more boys and 12 less girls then the ratio would have been 2:1.

To Find:-

  • No. of students in the the class

Solution:-

Let no. of boys and girls be 4x and 3x respectively.

As it's given that,

  • 4x + 20 : 3x - 12 = 2 : 1

On Solving this,

\implies\:\dfrac{4x+20}{3x-12}=\dfrac{2}{1}

On Cross Multiplication,

\implies\:4x+20=2(3x-12)

\implies\:4x+20=6x-24

\implies\:4x-6x=-20-24

\implies\:-2x=-44

\implies\:x=\dfrac{-44}{-2}

\implies\:x=\dfrac{44}{2}

{\boxed{\implies\:x=22}}

  • No. of boys = 4x = 4×22 = 88

  • No. of Girls = 3x = 3×2 = 66

⟹ Total Students = No. of (Boys + Girls)

⟹ Total Students = (88 + 66)

⟹ Total Students = 154

Hence, There are 154 students in the class 10 of the school.

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