Question

the number of female workers is twice the number of male workers in a factory. the factory owners pays ₹200 per day to each female worker and 300₹ per day to each male worker. if he paid a total of ₹75600 to all the workers, find the number of male and female workers in the factory​

Answer 1

★ Concept

The above question is based on Basic Algebra. Let's understand the question first, it's given that in a factory, the number of female workers is twice the number of male workers so, let's assume the number of Male workers be 'x' in that case, the number of female workers would be '2x'. Furthermore, it's given that the factor owner pays ₹ 200 to each female worker and ₹ 300 to each male worker [1 female worker = ₹ 200 and 1 Male worker = ₹ 300] per day. We'll first find out how much amount the factory owner pays to the total number of female workers (i.e ₹ 400x) similarly, the amount, the owner pays to the total number of male workers (i.e ₹ 300x.) According to our assumption, the owner pays ₹ 700x per day, at total, to all the workers but as per the question, it's already stated there that the owner pays ₹ 75600 to all the workers. On equating both the conditions, we will get the value for x [the total number of male workers] and so does the number of female workers (twice the value for x)

Let's proceed with Calculation !!

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Let the number of Male workers be 'x'

The number of female workers = 2x .

[The number of female workers is twice the number of male workers in a factory].

✪ According to the question

The Owner pays ₹ 200 to each Female worker.

Amount received by 1 female worker = ₹ 200

Total number of female workers = 2x

Total amount received by '2x' female workers

$\sf = Rs.(200 \times 2)x \quad \: = \: \underline{\boxed{\red{ \bf \: Rs. \: 400 \: x}}}$

The Owner pays ₹ 300 to each Male worker.

Amount received by 1 male worker = ₹ 300.

Total number of Male workers = x

Total amount received by 'x' male workers

$\sf = Rs.(300 \times x) \quad \: = \: \underline{\boxed{\red{ \bf\: Rs. \: 300 \: x}}}$

Also, it's given that he (the Owner) paid a total of ₹ 75600 to all the workers. Thus,

$\rm \mapsto Rs.(400x + 300x) = Rs. \: 75600$

$\sf \mapsto Rs. \: 700x = Rs. \: 75600$

$\rm \: x = \cancel\dfrac{75600}{700} \qquad \underline{\boxed{\bf{ \purple{ x = 108}}}}$

∴ Number of Male workers (x) = 108

Number of Female workers (2x) = 216

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Additional Information

In order to verify our result (to check output) we will now use the values for the number of Male and Female workers and will calculate the total number of wages, if it comes out to be ₹ 75600 our answer is correct (or verified).

» Number of Male workers = 108

» Number of Female workers = 216

The Owner pays ₹ 200 to each female worker (per day) so at total he pays ₹ (216 × 200) to all female workers i.e ₹ 43200 . Similarly, the Owner pays ₹ (108 × 300) to all Male workers i.e ₹ 32400.

This means at total, he pays ₹ (43200 + 53400) i.e ₹ 75600 to all the workers and that's what is given in the question.

Hence, Verified !!

Answer 2

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♦ Concept ➜

hello !!

your concept is based on the topic Basic Algebra in this question we are given that in a perticular factory the number of female worker are twice the number of male worker we are also given that the factory owner pays ₹200 per day to each female worker and 300₹ per day to each male worker. Now the question is asking that find the number of male and female workers in the factory if factory owner paid a total of ₹75600 to all the workers. So let us suppose the number of male worker be (X) while the number of female worker be (2x).

let's start calculation !

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♦ Solution ➜

⟹ Male worker = x

⟹ Female worker = 2x

⟹ per male worker salary = 300

⟹ per female worker salary = 200

⟹ total money received = 75600

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⟹ So

⟹ X × 300 + 2x × 200 = 75600

⟹ 300x + 400x = 75600

⟹ 700x = 75600

⟹ Rs.75600

$⟹\sf \: x = \frac{75600}{700}=108$

⟹ Hence male worker is = $\tt\fbox\red{108}$

⟹ female worker = 2 × 108 = $\tt\fbox\red{216}$

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♦ Verification ➜

Total amount paid to female worker

⟹ No. female worker × amount paid per day

⟹ 216 × 200

$\tt\fbox\red{⟹ 43200}$

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Total amount paid to male worker

⟹ No. male worker × amount paid per day

⟹ 108 × 300

$\tt\fbox\red{⟹ 32400}$

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⟹ Total amount

⟹ male worker amount + female worker amount

⟹ 43200 + 32400

$\tt\fbox\red{⟹ 75600}$

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♦ Answer ➜

finally we conclude that the number of male worker and female worker

• male worker → 108
• female worker → 216

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