Planning an Examination Centre Under Capacity and Staffing Limits
A district examination centre must seat candidates for a morning paper. It has three halls: Hall A with 180 seats, Hall B with 120 seats, and Hall C with 90 seats. A furniture check finds that 10 per cent of Hall B's seats have broken desks and cannot be used. The standing rule is one invigilator for every 30 candidates or part thereof, plus one reserve invigilator per hall in use. Fourteen staff members have been assigned to the centre. The controller expects about 15 per cent absenteeism but insists that seating and staffing must be planned on registered strength, not expected attendance, because roll numbers are printed in advance. A fourth room, the library, can hold 45 candidates if needed. The centre has been asked whether it can accept 420 registrations.
1. Calculate the usable seating capacity of the three halls and the number of invigilators required if the centre is filled to that capacity.
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Hall A provides 180 usable seats. Hall B loses 10 per cent of 120, i.e. 12 seats, leaving 108. Hall C provides 90. Total usable capacity = 180 + 108 + 90 = 378 seats. Staffing is based on the rule 'one per 30 candidates or part thereof', so divide 378 by 30: 12.6, which rounds up to 13 invigilators. Then add one reserve per hall in use: three halls, so three reserves. Required strength = 13 + 3 = 16 invigilators. With only 14 staff assigned, the centre is short by 2 invigilators even before considering the 420 registrations. The rounding step matters: treating 12.6 as 12 would under-staff the last group of 18 candidates.
2. Can the centre accept 420 registrations? If not, what is the minimum additional arrangement needed?
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No. Usable capacity is 378, so 420 registrations exceed it by 42 seats. The library holds 45, which is sufficient seating, but opening it changes the staffing calculation. With 420 candidates: 420 ÷ 30 = 14, so 14 invigilators, plus one reserve for each of four halls = 4, giving 18 invigilators. Only 14 are assigned, so the centre would need 4 more staff as well as the library. If four extra staff cannot be found, the centre cannot legally accept 420 under its own staffing rule. The practical options are to cap registrations at 378, shift 42 candidates to another centre, or obtain four additional invigilators and formally open the library as a fourth hall.
3. A clerk argues that because 15 per cent will be absent, only about 357 candidates will appear, so the 14 assigned invigilators are enough. Evaluate this argument.
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The arithmetic is right but the conclusion is wrong. Fifteen per cent of 420 is 63, so expected attendance is 357. At 357 candidates, 357 ÷ 30 = 11.9, which rounds up to 12 invigilators, plus four hall reserves if the library is used = 16, still above 14. Even if the library is not used and attendance is squeezed into three halls, 12 + 3 = 15, still one short. More fundamentally, the controller has already ruled that staffing must follow registered strength because absenteeism is an estimate, not a guarantee. If turnout is higher than expected, the centre would breach the invigilation ratio. The clerk's approach saves staff on paper but creates a compliance risk on the day.