Difficulty: Medium
Correct Answer: ₹ 29
Explanation:
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:
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
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