Question

Two hundred employee work for a company where the ratio of men to women is 11:9. If 30 men leave the company and 10 women are hired what is the new ratio of men to women?

A) 4 :5 B) 5:4 C) 11:9 D) 9:10
explaintion
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with explantion thank and brainliest wil be marked

Answer 1

Answer :-

$\: \\ \: \boxed{\boxed{\rm{\mapsto \: \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of Ratios of Value has been used. We see that initial ratio of men to women is given. We see that its divided by a constant. So we can take that as variable. We are also given with total number of employees. Equating that we can find the initial number of men to women. And then we can apply the case and find the value.

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★ Formula Used :-

$\: \\ \: \large{\boxed{\boxed{\sf{11x \: + \: 9x \: \: = \: \: \bf{200}}}}}$

$\: \\ \: \large{\boxed{\boxed{\sf{Initial \: Number \: of \: each \: person_{(male \: or \: female)} \: \: = \: \: \bf{Ratio \: part \: \times \: \: The \: Value \: of \: x}}}}}$

$\: \\ \: \large{\boxed{\boxed{\sf{Final \: Ratio \: of \: men \: to \: women \: = \: \bf{\dfrac{New \: number \: of \: males}{New \: number \: of \: females}}}}}}$

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★ Question :-

Two hundred employee work for a company where the ratio of men to women is 11:9. If 30 men leave the company and 10 women are hired what is the new ratio of men to women?

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★ Solution :-

Given,

» Total number of employees = 200

» Initial Ratio of Men to Women = 11 : 9

» Reduction in number of males = 30 men

» Increase in number of females = 10 women

Let x be the constant by which both initial number of males and females should be multiplied.

• Initial number of males = 11x

• Initial number of females = 9x

So according to the question :-

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~ For the value of x :-

$\: \\ \qquad \: \large{\sf{\Longrightarrow \: \: \: (Initial \: number \: of \: males) \: + \: (Initial \: number \: of \: females) \: \: = \: \: \bf{200}}}$

$\: \\ \qquad \: \large{\sf{\Longrightarrow \: \: \: 11x \: + \: 9x \: \: = \: \: \bf{200}}}$

$\: \\ \qquad \: \large{\sf{\Longrightarrow \: \: \: 20x \: \: = \: \: \bf{200}}}$

$\: \\ \qquad \: \large{\sf{\Longrightarrow \: \: \: x \: \: = \: \: \bf{\dfrac{\cancel{200}}{\cancel{20}} \: \: = \: \: \underline{\underline{10}}}}}$

$\: \\ \: \large{\boxed{\boxed{\tt{Value \:\; of \;\: x \;\: = \: \bf{10}}}}}$

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~ For the Initial Number of Males and Females :-

$\: \\ \: \large{\sf{\longrightarrow \: \: \: Initial \: Number \: of \: each \: person_{(male \: or \: female)} \: \: = \: \: \bf{Ratio \: part \: \times \: \: The \: Value \: of \: x}}}$

$\: \\ \: \large{\sf{\longrightarrow \: \: \: Initial \: Number \: of \: Males \: \: = \: \: \bf{11 \: \: \times \: \: 10 \: \: = \: \: \underline{\underline{\boxed{\bf{110 \: males}}}}}}}$

$\: \\ \: \large{\sf{\longrightarrow \: \: \: Initial \: Number \: of \: Males \: \: = \: \: \bf{9 \: \: \times \: \: 10 \: \: = \: \: \underline{\underline{\boxed{\bf{90 \: females}}}}}}}$

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~ For the final number of Males and Females :-

➣ Final number of males = 110 - 30

= 80

➣ Final number of females = 90 + 10

= 100

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~ Ratio of Final Number of Males and Females :-

$\: \\ \: \large{\sf{:\Longrightarrow \: \: \: Final \: Ratio \: of \: men \: to \: women \: = \: \bf{\dfrac{New \: number \: of \: males}{New \: number \: of \: females}}}}$

$\: \\ \: \large{\sf{:\Longrightarrow \: \: \: Final \: Ratio \: of \: men \: to \: women \: = \: \bf{\dfrac{\cancel{80}}{\cancel{100}} \: \: = \: \: \boxed{\dfrac{4}{5}}}}}$

$\: \\ \: \large{\boxed{\boxed{\tt{Final \:\; Ratio \:\; Males \;\: to \:\; Females \;\: = \: \bf{4:5}}}}}$

$\: \\ \large{\underline{\underline{\sf{Thus \: the \: new \: ratio \: of \: males \: to \: females \: is \: \: \boxed{\underline{\bf{4 \: : \: 5}} \: \: \: \: \: \sf{Option \: \: A}}}}}}$

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$\: \\ \: \large{\underline{\sf{\leadsto \: \: \: Confused?, \: Don't \: worry \: Let's \: Verify \: it \: :-}}}$

For verification we need to simply apply the values we got into the equations we formed. Then,

=> 11x + 9x = 200

=> 110 + 90 = 200

=> 200 = 200

Clearly, LHS = RHS.

Here the condition satisfies, so our answer is correct.

Hence, Verified

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$\: \: \\ \large{\underbrace{\underbrace{\rm{Let's \: \: Understand \: \: More \: \: :-}}}}$

• Algebra is terms used to denote the variable and constant part in the equations.

• Linear Equations are the equations formed using constant and variable terms but of single degrees of variables.

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Answer 2

Given :

Two hundred employee work for a company where the ratio of men to women is 11:9. If 30 men leave the company and 10 women are hired

To find :

New ratio of men to women?.

Solution :

Let the number of employees be 11m and 9m

Now atq,

⇒ 11m + 9m = 200

⇒ 20m = 200

⇒ m = 200/20

⇒ m = 10

Now 30 men leave and 10 women are hired.

So new number of employees :

⇒ Number of men working = 11m - 30

⇒ Number of women working = 9m + 10

So new ratio of men to women :

⇒ New ratio = (11m - 30) : (9m + 10)

⇒ New ratio = (11 * 10 - 30) : (9 * 10 + 10)

⇒ New ratio = (110 - 30) : (90 + 10)

⇒ New ratio = 80 : 100

⇒ New ratio = 4 : 5

Therefore,

New ratio of men to women = 4 : 5    [Option A]