Question

एक कक्षा में लड़कियों की संख्या लड़कों से
20% अधिक है कक्षा में छात्रों की कुल संख्या 66 है।
। यदि कक्षा में 4 लड़कियाँ और आ जाये तो लडके तथा
लडकियों की कुल संख्या का अनुपात क्या होगा?​

Answer 1

AnswEr : [Eng.version]

3:4

$\bf{\large{\green{\underline{\bf{Given\::}}}}}$

In a class the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class.

$\bf{\large{\red{\underline{\bf{To\:find\::}}}}}$

The ratio of the number of the boy's of that girl's.

$\bf{\large{\green{\underline{\underline{\tt{Explanation\::}}}}}}$

Let the ratio of boy's be r

Let the ratio of girl's be m

$\bf{\large{\underline{\underline{\tt{\red{A.T.Q.\::}}}}}}$

$\dashrightarrow\tt{m\:=\:r+20\%\:of\:boy's}\\\\\\\dashrightarrow\tt{m\:=\:r+\frac{20}{100} *r}\\\\\\\dashrightarrow\tt{m\:=\:\dfrac{100r+20r}{100} }\\\\\\\dashrightarrow\tt{m\:=\:\cancel{\frac{120}{100}r }}\\\\\\\dashrightarrow\tt{\red{m\:=\:\dfrac{6r}{5} ..............................(1)}}$

Now,

$\dashrightarrow\tt{r+m=66}\\\\\\\\\dashrightarrow\tt{r+\dfrac{6r}{5} =66\:\:\:\:\:\:\:\:[from(1)]}\\\\\\\\\dashrightarrow\tt{\dfrac{5r+6r}{5} =66}\\\\\\\\\dashrightarrow\tt{5r+6r=66*5}\\\\\\\\\dashrightarrow\tt{11r\:=\:330}\\\\\\\\\dashrightarrow\tt{r\:=\:\cancel{\dfrac{330}{11} }}\\\\\\\\\dashrightarrow\tt{\red{r\:=\:30\:boy's}}$

$\bf{\large{\underline{\underline{\rm{Putting\:the\: value \:of\:r\:in\:equation\:(1),we\:get;}}}}}}}}$

$\dashrightarrow\tt{m\:=\:\dfrac{6}{\cancel{5}} *\cancel{30}}\\\\\\\\\dashrightarrow\tt{m\:=\:\big(6\times 6\big)}\\\\\\\\\dashrightarrow\tt{\red{m\:=\:36\:girl's}}$

∴ 4 girl's are admitted to the class :

$\leadsto\sf{New\:girl\:(m_{n})=(36+4)\:girl's}\\\\\leadsto\sf{m_{n}=40\:girl's}}$

Now,

$\bf{\large{\underline{\underline{\rm{\green{\blacksquare{\rm{The\:ratio\:of\:the\:boy's\:and\:girl's,we\:get;}}}}}}}}$

$\longrightarrow\tt{r\::\:m_{n}\:=\:30\::\:40}\\\\\\\longrightarrow\tt{\dfrac{r}{m_{n}} \:=\:\dfrac{3\cancel{0}}{4\cancel{0}} }\\\\\\\longrightarrow\tt{\green{\dfrac{r}{m_{n}} \:=\:\dfrac{3}{4} }}$

∴ The ratio of the boy's and girl's is 3:4 .