Numbers employed and wage ratios: Men, women, and children are employed in the proportion 3 : 2 : 1, and their daily wage rates are in the ratio 5 : 3 : 2 respectively. When 90 men are employed, the total daily wages paid to all (men + women + children) amount to ₹ 10,350. What is the daily wage of one man?

Introduction / Context:
This item combines headcount proportions with wage-rate ratios. Knowing the men:woman:child staffing proportion and their wage ratios allows us to set up the total daily wage equation and solve for the man’s daily wage explicitly.

Given Data / Assumptions:

• Headcount ratio = 3 : 2 : 1
• Wage-rate ratio (per day) = 5 : 3 : 2
• Men employed = 90
• Total daily wages for all categories = ₹ 10,350

Concept / Approach:
If 3 units correspond to 90 men, the scaling factor is 30. Therefore, there are 60 women and 30 children. If the base wage unit is x, man = 5x, woman = 3x, child = 2x. Form the total daily payout and solve for x, then compute 5x.

Step-by-Step Solution:
Women = 60, Children = 30Total per day = 90*(5x) + 60*(3x) + 30*(2x) = 450x + 180x + 60x = 690x690x = 10,350 ⇒ x = 15Man’s daily wage = 5x = 5 * 15 = ₹ 75

Verification / Alternative check:
Compute women and children wages: women = 60*45 = 2700, children = 30*30 = 900; men = 90*75 = 6750. Sum = 6750 + 2700 + 900 = 10,350.

Why Other Options Are Wrong:
₹ 45 is the woman’s wage at x = 15; ₹ 57.50 or ₹ 115 do not match any derived category at this x.

Common Pitfalls:
Confusing headcount and wage ratios; forgetting to scale the staffing counts using the 3 : 2 : 1 ratio.

Final Answer:
₹ 75