Men, women and children are employed to do a work in the proportion of 3 : 2 : 1 and their wages as 5 : 3 : 2. When 90 men are employed, total daily wages of all amounts to ₹ 10350. Find the daily wages of a man.

Let the numbers of men, women and
children are 3k, 2k and k, respectively.
Given, 3k = 90
⇒ k = 30
Number of women = 60
and number of children = 30
Let the men's, women's and children's
wages be ₹ 5p, ₹ 3p and ₹ 2p, respectively.
According to the question,
Total daily wages = ₹ 10350
⇒ 90 x 5p + 60 x 3p + 30 x 2p = 10350
⇒ p x (450 + 180 + 60) = 10350
∴ p = 10350/690 = 15
∴ Daily wages of a man = 15 x 5 = ₹ 75