Question

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​

Answer 1

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

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

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

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

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

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

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

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

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

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

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

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

$\sf\large{Hence,}$

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

Answer 2

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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