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

2 thoughts on “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”

1. [tex]\sf\small\underline\purple{Let:-}[/tex]

   [tex]\tt{\implies Number\:of\:boys=4x}[/tex]

   [tex]\tt{\implies Number\:of\: girL=3x}[/tex]

   [tex]\sf\small\underline\purple{Given:-}[/tex]

   [tex]\tt{\implies Ratio\:of\:boys\:to\:girls=4:3}[/tex]

   [tex]\sf\small\underline\purple{To\: Find:-}[/tex]

   [tex]\sf{\implies Number\:of\: students=?}[/tex]

   [tex]\sf\small\underline\purple{Solution:-}[/tex]

   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.

   [tex]\sf{\implies \dfrac{boys+20}{girls-12}=\dfrac{2}{1}}[/tex]

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

   [tex]\tt{\implies 4x+20=6x-24}[/tex]

   [tex]\tt{\implies 4x-6x=-24-20}[/tex]

   [tex]\tt{\implies -2x=-44}[/tex]

   [tex]\tt{\implies 2x=44}[/tex]

   [tex]\tt{\implies x=22}[/tex]

   • Now calculate the no of boys and girls

   [tex]\tt{\implies Number\:of\:boys=4x}[/tex]

   [tex]\tt{\implies 4\times\:22}[/tex]

   [tex]\tt{\implies 88\:boys}[/tex]

   [tex]\tt{\implies Number\:of\:girL=3x}[/tex]

   [tex]\tt{\implies 3\times\:22}[/tex]

   [tex]\tt{\implies 66\:girL}[/tex]

   • Now calculate total students

   [tex]\tt{\implies Total\:_{(student)}=Total\:_{(boys)}+Total\:_{(girL)}}[/tex]

   [tex]\tt{\implies Total\:_{(students)}=88+66}[/tex]

   [tex]\tt{\implies Total\:_{(students)}=154}[/tex]

   [tex]\sf\large{Hence,}[/tex]

   [tex]\bf{\implies Total\: number\:_{(students)}=154}[/tex]

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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,

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

   On Cross Multiplication,

   [tex]\implies\:4x+20=2(3x-12)[/tex]

   [tex]\implies\:4x+20=6x-24[/tex]

   [tex]\implies\:4x-6x=-20-24[/tex]

   [tex]\implies\:-2x=-44[/tex]

   [tex]\implies\:x=\dfrac{-44}{-2}[/tex]

   [tex]\implies\:x=\dfrac{44}{2}[/tex]

   [tex]{\boxed{\implies\:x=22}}[/tex]

   • 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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