Q60·CSAT · Prelims 2026

Quantitative — Linear Optimization Scenarios

NumericalAlgebra — Linear EquationsArithmetic Problem● Medium

Question

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? [cite: 4887, 4888, 4889, 4890, 4922, 4923, 4924, 4925]

Options

The question cannot be answered due to insufficient data

Answer

Explanation

Let x be the number of successful deliveries made, and d be the total distance traveled in kilometers during the day. [cite: 4887, 4889, 4923]

Formulate the earning expression: Total daily income is given by E = 5x + 2d. [cite: 4888, 4889, 4923]

Apply constraint boundaries: The delivery boy aims for E > 500, subject to the maximum travel limit d \le 100. [cite: 4890, 4924]

Analyze the worst-case scenario: To find a number of deliveries that will definitely guarantee meeting his target, we must test the worst-case condition where distance traveled is minimized (d = 0 km or close to zero, meaning multiple deliveries are clustered near the shop).

5x + 2(0) > 500 \implies 5x > 500 \implies x > 100 deliveries

If he completes 90 deliveries (option c) and travels the maximum 100 km, his earnings would be 5(90) + 2(100) = 450 + 200 = 650 (exceeding the target)[cite: 4888, 4889, 4890, 4923, 4924]. However, if he completes 90 deliveries but travels only 20 km total, his earnings drop to 450 + 40 = 490, which falls short of his 500 target[cite: 4888, 4889, 4923, 4924]. Because the actual distance traveled per delivery is an independent variable not fixed by the problem, no listed option can definitely guarantee success under all conditions, making the data insufficient.

Optimization problems that ask what will 'definitely' guarantee a target require testing the worst-case scenario parameters to see if the criteria are fully met under all conditions.

Answer: (d).

Question details

Year

2026

Paper

CSAT

Question

Q60

Section

Quantitative Aptitude

Sub-topic

Algebra — Linear Equations

Type

Arithmetic Problem

Difficulty

Medium

Source hint

Linear boundaries — calculating minimum integer thresholds

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