A man and a boy received ₹ 800 as wages for 5 days for the work they did together. The man's efficiency in the work was three times that of the boy. What are the daily wages of the boy? (S.S.C., 2005)

### Concept & Proportionality Wages are distributed in proportion to the work done. When the time spent working is identical for all individuals, their wages are directly proportional to their efficiencies. ### Step-by-Step Solution * **Total Wages:** The combined wages for 5 days = ₹ 800 * **Combined Daily Wage:** ₹ 800 / 5 = ₹ 160 * **Efficiency Ratio:** Man : Boy = 3 : 1 * **Wage Division:** Since they worked together for the same number of days, the daily wage of ₹ 160 is divided in the ratio 3 : 1. * Total parts = 3 + 1 = 4 parts. * The boy's share corresponds to 1 part out of the 4 total parts. * Boy's daily wage = $\frac{1}{4} \times 160 = 40$ ### Exam Strategy & Shortcut Calculate the total daily wage immediately: $800 \div 5 = 160$. Because the efficiency ratio is 3:1, there are 4 equal parts total. The boy gets 1 part. Simply divide $160 \div 4 = 40$. This skips unnecessary algebra. ### Common Pitfall A frequent error is dividing the total ₹ 800 directly by the efficiency ratio to get ₹ 200 for the boy, completely forgetting that this is the wage for 5 days, not a daily wage. ### Final Answer Therefore, the correct answer is **₹ 40**.