Question : The average daily income of 7 men, 11 women, and 2 boys is Rs. 257.50. If the average daily income of men is Rs. 10 more than that of women and the average daily income of women is Rs. 10 more than that of boys, then the average daily income of a man is:
Option 1: Rs. 277.5
Option 2: Rs. 250
Option 3: Rs. 265
Option 4: Rs. 257
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Correct Answer: Rs. 265
Solution :
Let per day income of a boy, woman, and man be $x, x+10,$ and $x+20,$ respectively.
According to the question,
$\frac{\text{Total income of (7 Men + 11 Women + 2 Boys)}}{20} = 257.50$
Putting the values, we get:
$7(x+20)+11(x+10)+2x = 257.50×20$
$⇒7x+140+11x+110+2x = 5150$
$⇒20x = 5150 - 250$
$⇒x = \frac{4900}{20}$
$\therefore x= 245$
$\therefore$ Average daily income of a man $ = x + 20 = 245 + 20 = 265$
Hence, the correct answer is Rs. 265.
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