Question

There are 56 students in clas 7. The ratio of the number of boys to the number of girls is 4:3. Find the number of boys and girls in the class
There are two answers in it 24 And 32

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Answer 1

AnswEr-:

$\mathrm {\bf{Given-:}}$

• There are 56 students in $7^{th}$ Class .

• The ratio of the number of boys to the number of girls is 4:3.

$\mathrm {\bf{To\:Find-:}}$

• The number of Boys and Girls in Class .

$\mathrm {\dag{ Solution \:of\:Question -:}}$

• $\mathrm{Let's \:Assume \:\: -:} \begin{cases} \sf{\blue{The\:number \:of\:boys\:be\:\:= \frak{4x }}} & \\\\ \sf{\red{ The\:number \:of\:girls\:be\:\:\:=\:\frak{3x}}}\end{cases}$

$\quad \qquad\quad \qquad\quad \qquad\quad \qquad\mathrm{\underline {\star{ Now ,\: According \:to\:the\:Given\:Question\;-:}}}$

$\mathrm {\bf{Given\:that-:}}$

• There are 56 students in $7^{th}$ Class .

Now ,

$\quad \qquad\quad \qquad\quad \qquad\quad \qquad:\implies {\mathrm { 4x + 3x = 56 }}$

$\quad \qquad\quad \qquad\quad \qquad\quad \qquad:\implies {\mathrm { 7x = 56 }}$

$\quad \qquad\quad \qquad\quad \qquad\quad \qquad:\implies {\mathrm { x = \dfrac{56}{7} }}$

$\quad \qquad\quad \qquad\quad \qquad\quad \qquad:\implies {\mathrm { x = \dfrac{\cancel {56}^{(8)}}{\cancel {7}} }}$

$\quad \qquad\quad \qquad\quad \qquad\quad \qquad\underline{\boxed{\pink {\frak { x = 8 }}}}$

$\mathrm { Now, \:By\:Putting\:x\:=\:8 -:}$

• $\mathrm{Putting \:x=8\:\:\: -:} \begin{cases} \sf{\blue{The\:number \:of\:boys\:be\:\:= \frak{4x= 4 \times 8 = 32 }}} & \\\\ \sf{\red{ The\:number \:of\:girls\:be\:\:\:=\:\frak{3x= 3 \times 8 = 24}}}\end{cases}$

$\mathrm {\bf{Hence -:}}$

$\underline{\pink{\mathrm { The\:number \:of\:boys\:and\:girls\:in\:7^{th}class\:is\:\bf{32}\:and\:\bf{24}\:respectively. }}}$

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$\Large{\boxed{\mathrm |\:\:\:{\underline {\dag{ Verification \:-:}}}\:\:\:|}}$

As , We know that -:

• $\boxed{\mathrm{\pink { Number\:of\:boys\:+\:Number\:of\:Girls\:=\:Total\:number\:of\:Student}}}$

$\mathrm { \bf{ Here-:}}$

• The number of Boys is 32 .

• The number of girls is 24 .

• The total number of Students is 56 .

Now by putting known Values-:

$\quad \qquad\quad \qquad\quad \qquad\quad \qquad:\implies {\mathrm { 32 + 24 = 56 }}$

$\quad \qquad\quad \qquad\quad \qquad\quad \qquad:\implies {\mathrm { 56 = 56 }}$

$\mathrm { \bf{ Therefore, }}$

$\quad \qquad\quad \qquad\quad\implies{\mathrm { \bf{ L.H.S = R.H.S }}}$

$\quad \qquad\quad \qquad\quad\implies{\mathrm { \bf{ Hence ,\:Verified!}}}$

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