Question

A class has 4 more girls than boys.On a day when only 8 boys were absent,the number of girls was twice that of the boys.How many girls and boys are there in the class?​

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given that a class have 4 more girls than boys
• When 8 boys were absent the number of girls was twice the number of boys

To Find:

• We have to find the number of boys and girls in the class

Solution:

Let number of boys = x

Number of Girls = y = x + 4

$\large\underline{\mathfrak\red{According \: of \: the \: Question}}$

When 8 boys were absent , the number of girls was twice the number of boys

$\implies \boxed{\sf{ y = 2( x - 8 )}}$

$\implies \sf{ y = 2x - 16 }$

Putting y = ( x + 4 ) in above Equation

$\implies \sf{x + 4 = 2x - 16 }$

$\implies \sf{2x - x = 16 + 4 }$

$\implies \boxed{\sf{ x = 20}}$

Hence the value of y is as follows

$\implies \sf{ y = 20 + 4 }$

$\implies \boxed{\sf{ y = 24} }$

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$\huge\underline{\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}}$

$\large\boxed{\sf{\red{Number \: of \: Boys = 20}}}$

$\large\boxed{\sf{\purple{Number \: of \: Girls = 24}}}$

_________________________________

$\huge\mathtt\green{Verification:}$

☞ Number of girls is 4 more than the number of boys in the class

$\implies \sf{Number \: of \: Boys + 4}$

$\implies \sf{20 + 4 }$

$\implies \sf{24 \: (\: Number \: of \: Girls \: )}$

☞ When 8 boys were absent the number of girls were twice the number of boys

$\implies \sf{2 \times ( \: No. \: of \: Boys - 8 \: ) }$

$\implies \sf{2 \times (20 - 8)}$

$\implies \sf{2 \times 12}$

$\implies \sf{24 \: (\: Number \: of \: Girls \: )}$

$\red{\large\underline{\underline{\sf{Hence \: Verified \: !!! }}}}$