Question

The employees in a certain factory are divided into three wage classifica
tion. One group is paid at the rate of Rs. 25 per day, a second group in
which there are twice as many employees as in the first group, is paid at
the rate of Rs. 40 per day, and a third group, in which there are half as
many employees as in the other two groups is paid Rs. 50 per day. If the
total daily pay roll is Rs. 5400, how many employees are there in each
group.​

Answer 1

AnswEr :

• Wages of First Group = Rs. 25
• Wages of Second Group = Rs. 40
• Wages of Third Group = Rs. 50

Let the Number of Employees in the First Group be x

• E M P L O Y E E S :

◗ First Group = x

◗ Second Group = 2x

◗ Third Group = $\sf\dfrac{x + 2x}{2} = \dfrac{3x}{2}$

$\rule{200}{1}$

• According to the Question Now :

$\implies \tt Employees \times Wages = Total \\ \\\implies \tt (x \times 25) + (2x \times 40) + \bigg(\dfrac{3x}{ \cancel2} \times \cancel{50} \bigg) = 5400 \\ \\\implies \tt 25x + 80x + (3x \times 25) = 5400 \\ \\\implies \tt 25x + 80x + 75x = 5400 \\ \\\implies \tt 180x = 5400 \\ \\\implies \tt x = \cancel\dfrac{5400}{180} \\ \\\implies \red{\tt x = 30}$

$\rule{300}{2}$

• N O. ⠀O F ⠀E M P L O Y E E S :

◗ First Group = x = 30

◗ Second Group = 2x = 2(30) = 60

◗ Third Group = $\sf\dfrac{3x}{2}=\dfrac{3(30)}{2}=\dfrac{90}{2}$ = 45

⠀

∴ Therefore, Number of Employees in the first, second and third Group will be 30, 60 and 45 respectively.

Answer 2

$\huge{\underline{\underline{\mathbb{Given}}}}$

→ 1st group's salary = rs 30 per day .

→ 2nd group's salary = rs 40 per day .

→ 3rd group's salary = rs 50 per day .

$\huge{\underline{\underline{\mathbb{Solution}}}}$

Relation between employees of these 3 groups is :-

～>Let employees of 1st group = x

～>Employees of 2nd group = double of 1st

double = 2x

～> Employees of 3rd group = half of sum of employees of 1st and 2nd group .

Sum = x + 2x = 3x

Total employees in 3rd group = 3x/2

Now , Let's talk about their salary

～> Total Salary of 1st group = 25( x )

～> Total salary of 2nd group = 40 ( 2x )

→ 80 x

～> Total salary of 3rd group = 50 ( 3x/2)

→ 25 × 3x = 75 x

Then sum of salary of all these three groups :-

25 x + 80 x + 75 x = 5400

180 x = 5400

x. = 30

____________________

Number of employees :-

→ 1st group = x

～>30 employees .

→ 2nd group = 2x

～>2×30

～>60 employees

→ 3rd group = $\frac{3x}{2}$

～>3×15

～> 45 employees