A, B and C are employed to do a piece of work for ₹ 529. A and B together are supposed to do $\frac{19}{23}$ of the work and B and C together $\frac{8}{23}$ of the work. What amount should A be paid ?

### Concept & Work Proportions and Wages Wages are distributed strictly in proportion to the actual amount of work done by each individual. $$ \text{Individual Share} = (\text{Fraction of Work Done}) \times \text{Total Pay} $$ ### Step-by-Step Solution * **Given:** Total contract amount = ₹ 529. Total work is considered as 1 complete unit. * Work done by (A + B) = $19/23$. * Work done by (B + C) = $8/23$. * We need to find A's share, which means we need the fraction of work done by A alone. * Since (B + C) do $8/23$ of the work, A must do the rest of the work to complete the total 1 unit. * Work done by A = Total Work - Work done by (B + C) A = $1 - 8/23$ A = $(23 - 8) / 23 = 15/23$ * So, A does $15/23$ of the total work. * Amount A should be paid = (A's fraction of work) $\times$ (Total amount) A's pay = $(15/23) \times 529$ * Since $23 \times 23 = 529$, this simplifies to: A's pay = $15 \times 23$ * $15 \times 23 = 345$. * A should be paid ₹ 345. ### Exam Strategy & Shortcut Recognize that finding A directly from subtracting $(B+C)$ from the total work is the fastest path. $1 - 8/23 = 15/23$. Since the denominator is 23 and the total pay is $23^2$ (529), calculation is straightforward: $15 \times 23$. For quick mental math: $15 \times 20 = 300$, $15 \times 3 = 45$. Total = 345. ### Common Pitfall Trying to find the individual work of all three (A, B, and C) before calculating the wage. Finding B and C is unnecessary to answer the specific question asked. ### Final Answer Therefore, the correct answer is **₹ 345**.