Question

19 ) The number of boys and girls in a class are in the ratio 3:8 . The number of girls is 20 more than the number of boys . What is the total strength ?​

Answer 1

Step-by-step explanation:

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Answer 2

GIVEN :–

• The number of boys and girls in a class are in the ratio 3:8 .

• The number of girls is 20 more than the number of boys .

TO FIND :–

• Total strength = ?

SOLUTION :–

• Let the number of boys = x

• And the number of girls = y

• According to the first condition –

$\\ \bf \implies \dfrac{x}{y} = \dfrac{3}{8}$

$\\ \bf \implies x= \dfrac{3}{8}y \: \: \: \: - - - - eq.(1)$

• According to the second condition –

$\\ \bf \implies y = x + 20 \: \: \: \: \: - - - - eq.(2)$

• Put the value of 'y' in eq.(1) –

$\\ \bf \implies x= \dfrac{3}{8}(x + 20)$

$\\ \bf \implies 8x=3(x + 20)$

$\\ \bf \implies 8x=3x + 60$

$\\ \bf \implies 8x - 3x = 60$

$\\ \bf \implies 5x = 60$

$\\ \bf \implies x = \cancel \dfrac{60}{5}$

$\\ \implies \large{ \boxed{ \bf x = 12}}$

• Using eq.(2) –

$\\ \bf \implies y = 12+ 20$

$\\ \implies \large{ \boxed{ \bf y =32}}$

• Now Total strength –

$\\ \implies \bf Total \: \: strength = x + y$

$\\ \implies \bf Total \: \: strength = 12 + 32$

$\\ \implies \large{ \boxed{ \bf Total \: \: strength =44}}$