A shopkeeper employs a delivery boy and gives him a motorcycle for home delivery. For every delivery, the boy is given ₹ $5$. At the end of the day, he also gets ₹ $2$ for every kilometre of the distance covered in the day. The boy wants to earn more than ₹ $500$ a day, but does not want to travel more than $100$ km. Which of the following numbers of deliveries would definitely meet his target?
Detailed Explanation:
Earnings formula: E = 5d + 2k, where d = deliveries and k = km travelled. Target: E > 500, with constraint k ≤ 100.
To definitely meet the target using d alone, the inequality must hold even in the worst case (k = 0), requiring 5d > 500 or d > 100. For the given options (d = 80, 85, 90), worst-case earnings are ₹400, ₹425, and ₹450 respectively—all fall short of ₹500. Since actual km travelled is unknown and could be anywhere from 0 to 100, none of the delivery counts guarantees the target.
Therefore, without knowing the distance covered, the question cannot be answered due to insufficient data, making Option 4 the correct answer.
Question 3 of 3 Linear Equations
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