Question

10. The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8
more than the number of girls. What is the total class strength?
explain in full solution​

Answer 1

$\large\underline{\underline{\frak{\qquad Given :\qquad}}}$

• The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls.

$\large\underline{\underline{\frak{\qquad To \: Find:\qquad}}}$

• Total class strength = ?

$\large\underline{\underline{\frak{\qquad Solution:\qquad}}}$

Let number of boys be 7x and number of girls be 5x.

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

• The number of boys is 8 more than the number of girls

$:\implies \sf Number \: of \: boys = Number \: of \: girls + 8$

$:\implies \sf 7x = 5x + 8$

$:\implies \sf 7x - 5x = 8$

$:\implies \sf 2x = 8$

$:\implies \sf x = \dfrac{8}{2}$

$:\implies \underline{ \boxed{ \sf x = 4 }}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━

$\bigstar\: \underline{\textsf{Finding number of boys in a class :}}$

$\dashrightarrow\:\:\sf Number \: of \: boy's = 7x$

$\dashrightarrow\:\:\sf Number \: of \: boy's = 7 \times 4$

$\dashrightarrow\:\: \underline{ \boxed{\sf Number \: of \: boy's = 28}}$

$\therefore\:\underline{\textsf{Total Number of boys in the class is \textbf{28}}}.$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━

$\bigstar\: \underline{\textsf{Finding number of girls in a class :}}$

$\dashrightarrow\:\:\sf Number \: of \: girl's = 5x$

$\dashrightarrow\:\:\sf Number \: of \: girl's = 5 \times 4$

$\dashrightarrow\:\: \underline{ \boxed{\sf Number \: of \: girl's = 20 }}$

$\therefore\:\underline{\textsf{Total Number of girls in the class is \textbf{20}}}.$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━

$\bigstar\: \underline{\textsf{Now, let's find the total strength of the class :}}$

$\longrightarrow\:\:\sf Total \: strength = Total \: number \: of \: boy's + Total \: number \: of \: girl's$

$\longrightarrow\:\:\sf Total \: strength = 28 + 20$

$\longrightarrow\:\: \underline{ \boxed{\sf Total \: strength = 48}}$

$\therefore\:\underline{\textsf{Total strength of the class is \textbf{48}}}.$

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Answer 2

Given:-

• Ratio of no. of boys and girls = 7:5
• No. of boys is 8more than the no. of girls.

Find:-

• Total strength of the class.

Solution:-

Let, The no. of boys be ❝7x❞

and, The no. of girls be ❝5x❞

◕ According To Question ◕

No. of boys is 8 more than the no. of girls

↬7x - 8 = 5x

↬7x - 5x = 8

↬2x = 8

↬x = 8/2

↬x = 4

• Now, No. Girls in a class:

➟ No. of girls = 5x

➟ No. of girls = 5×4

➟ No. of girls = 20

• No. of boys in a class:

➠ No. of boys = 7x

➠ No. of boys = 7×4

➠ No. of boys = 28

$\qquad$ ________________________

• Now, finding the total strength of the class:

➢ Total Class Strength = No. of boys + No. of girls

➢ Total Class Strength = 28 + 20

➢ Total Class Strength = 48

Hence, The Total strength of the class is 48