Time, Work & Wages Guide & Practice

Core Foundations

Fundamental Formulas

1. Work Relation: $\text{Work done} = \text{Time} \times \text{Efficiency}$
2. Efficiency: $\text{Efficiency} \propto \frac{1}{\text{Time taken}}$ (for the same work).
   • If A can do a work in $n$ days, A's 1-day work = $\frac{1}{n}$.
   • If A is $k$ times as efficient as B, Ratio of efficiency $A:B = k:1$; Ratio of time taken $A:B = 1:k$.
3. Group Work (MDH Formula): $\frac{M_1 D_1 H_1 E_1}{W_1} = \frac{M_2 D_2 H_2 E_2}{W_2}$ Where $M$=Men, $D$=Days, $H$=Hours, $E$=Efficiency, $W$=Work.

Efficiency as Percentage

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Thematic Deep-Dive

1. Two or More Persons Working Together

• Two Persons: If A takes $x$ days and B takes $y$ days, together they take $\frac{xy}{x+y}$ days.
• Three Persons: If A, B, and C take $x, y, z$ days, together they take $\frac{xyz}{xy+yz+zx}$ days.
• LCM Method: Assume total work as the LCM of individual days to find daily "units" of work.

2. Work and Wages

• Rule: Wages are distributed in proportion to the work done or efficiency (if time is the same).
• Ratio: $\text{Wages of A} : \text{Wages of B} = \text{Efficiency of A} : \text{Efficiency of B}$.

3. Alternate Days / Hours

• Find the combined work done in one "cycle" (e.g., 2 days for A then B).
• Divide total work by cycle work to find total cycles and remaining work.

4. Men, Women, and Boys

• Convert the group into a single unit (e.g., convert all into "equivalent men" or "equivalent boys").
• Use the relation $M_1D_1 = M_2D_2$ after conversion.
• Example: 12 Men = 24 Boys $\implies$ 1 Man = 2 Boys.

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