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?

The correct answer is Option D.

To determine the delivery boy's earnings, let the number of deliveries be 'x' and the distance covered in kilometres be 'y'. According to basic algebraic principles for linear equations, the earnings function is: Total Earnings = 5x + 2y

We are given two constraints:

1. Target earnings: 5x + 2y > 500
2. Maximum distance: y 500, meaning x > 100. Because the exact distance 'y' is an independent, unknown variable and no mathematical relation between the number of deliveries and distance is provided, the data is inherently insufficient to guarantee that any given number of deliveries under 100 will meet the target.

Why the other options are incorrect:

• Option A (80): If he makes 80 deliveries but travels 0 km, his baseline earnings would be ₹ 400, falling short of the target.
• Option B (85): At 85 deliveries with negligible distance, his earnings are ₹ 425, which does not definitively meet the > ₹ 500 target.
• Option C (90): 90 deliveries yield a baseline of ₹ 450. Without a known distance, it cannot be guaranteed to cross the ₹ 500 threshold.

Takeaway: In CSAT aptitude questions testing 'guarantees' or 'definitiveness', always evaluate the worst-case scenario by minimizing unknown variables. If the worst case fails, the outcome is not definitively guaranteed.