Equivalent wages across categories: The combined daily wages of 3 men, 2 women, and 4 boys is ₹ 26. Given that wages of 3 men equal wages of 4 women, and wages of 2 women equal wages of 3 boys, find the total daily wages for a group of 4 men, 3 women, and 2 boys.

Introduction / Context:We must reconcile wage relationships between men, women, and boys to a common unit and then compute the total for a different combination. Such problems rely on expressing all categories in terms of one variable using the given equivalences.

Given Data / Assumptions:

• 3 men = 4 women (in wages)
• 2 women = 3 boys (in wages)
• 3 men + 2 women + 4 boys = ₹ 26 (per day)
• Find: 4 men + 3 women + 2 boys

Concept / Approach:Let the daily wage of a woman be w. Then man's daily wage m and boy's daily wage b can be expressed in terms of w using the given equalities. Substitute into the known total to find w, then compute the requested combination.

Step-by-Step Solution:From 3m = 4w ⇒ m = 4w/3From 2w = 3b ⇒ b = 2w/3Total given: 3m + 2w + 4b = 3*(4w/3) + 2w + 4*(2w/3) = 4w + 2w + 8w/3 = 26w/326w/3 = 26 ⇒ w = 3Then m = 4, b = 2Desired: 4m + 3w + 2b = 4*4 + 3*3 + 2*2 = 16 + 9 + 4 = ₹ 29

Verification / Alternative check:Plug back: 3m + 2w + 4b = 12 + 6 + 8 = 26, consistent with the given total.

Why Other Options Are Wrong:₹ 35, ₹ 65, ₹ 20 do not result from the derived unit wages m = 4, w = 3, b = 2.

Common Pitfalls:Mistaking men–women equivalence as m = 3/4 w instead of m = 4/3 w; mixing wage and headcount proportions; arithmetic slips in fraction addition.

Final Answer:₹ 29