Question

The mean wage of 150 labourers working in a factory running three shifts with 60, 40 and 50 labourers is Rs 114.00 The mean wage of 60 labourers working in the first shift is Rs 121.50 and that of 40 labourers working in the second shift is Rs 107.75 then the mean wage of those working in the third shift is

• A. Rs 110
• B. Rs 100
• C. Rs 120
• D. Rs 115.75

Answer 1

Answer: (A)

Rs 110

Let the total wages of laborers working in shift 1 is x

Let the total wages of laborers working in shift 2 is y

Let the total wages of laborers working in shift 3 is z

Mean wages of 150 laborers =$\frac{x+y+z}{a+b+c}$

Where a, b and c is the number of laborers working is shift 1,2 and 3 respt

Mean wages =114 Rs

$\therefore \frac{x+y+z}{150}=114\Rightarrow x+y+z=114\times 150=17100$

Mean wages of laborers in shift 1 is=$\frac{x}{a}=121.5\Rightarrow x=121.5\times 60=7290$ ( a=60)

Mean wages of laborers in shift 2 is=$\frac{y}{b}=107.75\Rightarrow x=107.75\times 40=4310$ ( a=40)

(x+y+z)=17100

Or 7290+4310+z=17100 Or z=17100-7290-4310=5500

Let the mean of laborers in shift 3=c

$\therefore m=\frac{z}{c}=\frac{5500}{50}=110$ Rs

Then mean wage of laborer working in third shift=Rs 110