A labourer was engaged for 20 days on the condition that he will receive ₹ 60 for each day he works and he will be fined ₹ 5 for each day he is absent. If he received ₹ 745 in all, then the number of days on which he remained absent is

### Concept & Strategy This is an "Assumed Extreme" or deviation problem. To find the number of absent days, assume the worker was present for all days, calculate the maximum possible earnings, and divide the "lost" amount by the true cost of an absence. $$ \text{True Cost of Absence} = \text{Daily Wage Forfeited} + \text{Penalty Imposed} $$ ### Step-by-Step Solution * **Calculate Maximum Possible Earnings:** If the labourer worked all 20 days, he would earn $20 \times 60 = 1200$. * **Calculate Total Amount Lost:** He actually received 745. * Total loss = $1200 - 745 = 455$. * **Calculate the Cost of One Absent Day:** When he misses a day, he does not just pay a ₹ 5 fine; he also *loses* the ₹ 60 he would have earned. * Total cost per absent day = $60 (\text{lost wage}) + 5 (\text{fine}) = 65$. * **Calculate Number of Absent Days:** Divide the total amount lost by the cost of one absent day. * Absent days = $\frac{455}{65}$. * Simplify the division: $455 / 5 = 91$, and $65 / 5 = 13$. * $91 / 13 = 7$. ### Exam Strategy & Shortcut Using standard algebra also works quickly: Let $x$ be the days absent. Days present = $20 - x$. Equation: $60(20 - x) - 5x = 745$. $1200 - 60x - 5x = 745$ $1200 - 65x = 745$ $65x = 455 \rightarrow x = 7$. The key in both methods is recognizing the $65x$ factor. ### Common Pitfall The most frequent error is assuming the cost of an absence is just the ₹ 5 fine. This leads to the incorrect equation $1200 - 5x = 745$, resulting in $x = 91$, which is impossible for a 20-day job. You must account for the opportunity cost of the lost wage. ### Final Answer **Therefore, the correct answer is 7.**