Question : A company employed 700 men and 300 women and the average wage was Rs.450 per day. If a man got Rs.50 more than a woman, then the daily wage of the woman is:
Option 1: Rs. 350
Option 2: Rs. 375
Option 3: Rs. 415
Option 4: Rs. 435
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Correct Answer: Rs. 415
Solution :
Number of men = 700
Number of women = 300
The average wage of men and women combined = Rs. 450
Let the average wage of women be Rs. $x$.
Average wage of men = Rs. ($x+50$)
We know the sum of wages = Average wage × Total count of people
So, the sum of wages of women = $x$ × 300
And, the sum of wages of men = $(x+50)$ × 700
Now, Average wage of all people = $\frac{\text{Total Sum of wages}}{\text{Count of people}}$
⇒ 450 = $\frac{300x + 700(x+50)}{300+700}$
⇒ $ 450 \times 1000 = 1000x + 35000$
⇒ $1000x = 415000$
⇒ $x=415$
Hence, the correct answer is Rs. 415.
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