UPSC Prelims 2026 CSAT Paper II · Q80 of 70 Basic Numeracy easy

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?

  1. (a) 80
  2. (b) 85
  3. (c) 90
  4. (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.

Reading the answer is not the same as getting it right under a clock. Practise this question with UPSC's negative marking, and anything you miss goes into an error notebook until you get it right twice.

Practise this paper free