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If 6 machines produce 120 items in 8 hours, how many items can 9 machines produce in 4 hours at the same rate?
120
80
90
60
90
To solve this, use the work-time formula: (M1 * T1) / W1 = (M2 * T2) / W2, where M is machines, T is time, and W is work. Given 6 machines and 8 hours produce 120 items, the rate per machine-hour is 120 / (6 * 8) = 2.5 items; applying this to 9 machines for 4 hours yields 9 * 4 * 2.5 = 90 items.
To solve this, use the work-time formula: (M1 * T1) / W1 = (M2 * T2) / W2, where M is machines, T is time, and W is work. Given 6 machines and 8 hours produce 120 items, the rate per machine-hour is 120 / (6 * 8) = 2.5 items; applying this to 9 machines for 4 hours yields 9 * 4 * 2.5 = 90 items.
The principle of unitary method is fundamental to Quantitative Aptitude in Indian competitive exams, appearing frequently in Staff Selection Commission (SSC) and UPSC CSAT papers under Data Interpretation and Arithmetic sections.
Machine productivity is directly proportional to both the number of machines and the operating time.
Constant rate of production ensures that the ratio (Items / (Machines * Hours)) remains invariant.
Total items produced = Rate per machine-hour * Number of machines * Total time.
Unitary method allows for quick calculation of work efficiency by determining the output of a single unit (machine) per unit time (hour).
Option A (120) is incorrect as it assumes productivity remains constant despite changes in machine count and time.
Option B (80) arises from failing to adjust for the increase in machine count from 6 to 9.
Option D (60) incorrectly halves the production, ignoring the contribution of the additional machines.
C is correct тАФ 9 machines working for 4 hours produce 90 items based on the established production rate of 2.5 items per machine-hour.
The unitary method used here is directly applicable to 'Pipes and Cisterns' and 'Time and Work' problems, which constitute approximately 15 percent of the quantitative aptitude syllabus in government recruitment exams.
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