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?
- (a) 80
- (b) 85
- (c) 90
- (d) The question cannot be answered due to insufficient data ✓ UPSC's answer
Why the answer is (d)
["- The boy's total daily earnings are calculated as (5 × number of deliveries) + (2 × distance covered in km).", '- The problem states he wants to earn more than ₹500, so the inequality is 5D + 2K > 500, where D is deliveries and K is distance.', '- The constraint is that the distance K must be less than or equal to 100 km (K ≤ 100).', '- To find the minimum number of deliveries required, we must consider the maximum possible distance, as this contributes the most to the earnings from the distance component.', '- Even if he travels the maximum allowed 100 km, the earnings from distance are 2 × 100 = ₹200.', '- Therefore, the earnings from deliveries must be greater than 500 - 200 = ₹300, meaning 5D > 300, or D > 60.', '- However, the question asks which number of deliveries would *definitely* meet the target regardless of the distance traveled (as long as it is ≤ 100 km).', '- If he travels 0 km, he needs 5D > 500, so D > 100. Since the maximum distance is 100 km, the minimum distance is 0 km.', '- Because the distance traveled is not fixed and can vary between 0 and 100 km, a specific number of deliveries (like 80, 85, or 90) does not *definitely* guarantee more than ₹500 if the distance is low enough.', '- For example, if he makes 90 deliveries (₹450) and travels only 25 km (₹50), his total is ₹500, which is not *more than* ₹500.', '- Since the distance is a variable that is not specified, we cannot determine a single number of deliveries that *definitely* meets the target for all possible distances within the limit.', '- Thus, the question cannot be answered due to insufficient data regarding the actual distance traveled.']
Why the other options are wrong
- (a) 80
- 80 deliveries yield ₹400 from deliveries; if the distance is less than 50 km, total earnings will not exceed ₹500.
- (b) 85
- 85 deliveries yield ₹425 from deliveries; if the distance is less than 37.5 km, total earnings will not exceed ₹500.
- (c) 90
- 90 deliveries yield ₹450 from deliveries; if the distance is less than 25 km, total earnings will not exceed ₹500.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.