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A building contractor employs 25 male and 15 female workers. To a male worker he pays ₹20 per hour and to a female worker ₹20 per hour. The average wage per hour paid by the contractor is:
₹22
₹23
₹20
₹21
₹20
Since both male and female workers earn the same amount per hour (₹20), the weighted average must be exactly ₹20 regardless of the number of workers.
Number of male workers = 25, Wage per hour for male = ₹20. Number of female workers = 15, Wage per hour for female = ₹20.
Average=Total WorkersTotal Wage=∑ni∑(ni×wi)
Since both male and female workers earn the same amount per hour (₹20), the weighted average must be exactly ₹20 regardless of the number of workers.
Students often waste time calculating total wages (25×20+15×20=500+300=800) and total workers (25+15=40) then dividing, even though the result is obvious by inspection.
Identify given variables
We have nm=25 males earning wm=20 and nf=15 females earning wf=20.
nm=25,wm=20,nf=15,wf=20
Apply average formula
Total wages are calculated by multiplying the number of each group by their respective hourly wage, then dividing by the total count of workers.
Avg=25+1525×20+15×20
Calculate and simplify
Factoring out 20 from the numerator gives 20×(25+15)/(25+15), which simplifies to 20.
Avg=4020×(25+15)=4020×40=20
C is correct because since every worker earns the same hourly rate of ₹20, the weighted average is simply ₹20.
This logic applies to all 'weighted average' problems: if all items share the same value (like speed, price, or wage), the average is simply that value, regardless of the distribution proportions.
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