Quantitative Aptitude / Numerical Ability - Bridging a Weekly Claims Target at an ESIC Branch
An ESIC branch office works eight hours a day, six days a week, and currently employs eight clerks. On a full working day each clerk clears 24 claims, and output is strictly proportional to hours worked. Attendance records for the past year show that, on average, exactly one of the eight clerks is absent on any working day. The regional office has now fixed a weekly target of 1,440 claims. The branch manager has three ways to bridge the gap: engage temporary clerks, who clear the same 24 claims a day and cost ₹4,200 each per week; authorise overtime, which costs ₹210 per clerk per hour; or use a mix of both. Overtime cannot exceed two hours per clerk per day, and audit notes show that error rates climb steeply beyond that limit. Temporary staff can be hired only in whole numbers and only for complete weeks.
1. What is the branch's present weekly capacity, and how large is the weekly gap against the 1,440-claim target?
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Step 1 - effective strength. Eight clerks are on the roster, but the established pattern is one absentee a day, so plan on 7 clerks present.
Step 2 - daily output. 7 × 24 = 168 claims a day.
Step 3 - weekly output. The office works six days: 168 × 6 = 1,008 claims a week.
Step 4 - gap. 1,440 − 1,008 = 432 claims a week.
Note the two traps in this calculation. First, using all eight clerks (8 × 24 × 6 = 1,152) overstates capacity by exactly the absentee's week of work and would understate the gap as 288. Second, converting the target into a daily figure (1,440 ÷ 6 = 240 a day) is useful for cross-checking: the branch needs 240 − 168 = 72 extra claims daily, which is the same 432 over six days.
So the manager must add 432 claims of weekly capacity - not 288 - before any option is compared.
2. Compare (a) three temporary clerks and (b) two temporary clerks plus two hours of daily overtime per clerk. Which should the manager choose, and why?
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Option (a) - three temporaries.
- Output: 3 × 24 × 6 = 432 claims, exactly the gap, taking the branch to 1,440.
- Cost: 3 × ₹4,200 = ₹12,600.
- Overtime used: nil, so no quality risk.
Option (b) - two temporaries plus two hours' overtime.
- Temporaries: 2 × 24 × 6 = 288 claims.
- Overtime: each clerk clears 24 ÷ 8 = 3 claims an hour. Seven present clerks × 2 hours × 3 claims × 6 days = 252 claims.
- Total added: 288 + 252 = 540 claims, giving 1,548 - a surplus of 108 claims.
- Cost: ₹8,400 (temporaries) + 7 × 2 × 6 = 84 overtime hours × ₹210 = ₹17,640, total ₹26,040.
Judgement. Option (b) costs more than double option (a) and produces surplus output the branch does not need, while pushing every clerk to the two-hour ceiling where the audit found error rates rising. Option (a) meets the target exactly at zero overtime. Also check the tempting shortcut of four temporaries: 576 claims at ₹16,800 - still dearer than three. Recommendation: hire three temporaries.
3. If average absenteeism doubles to two clerks a day, does the recommendation change? Show the revised arithmetic.
Read the worked answer
Revised base. Six clerks present daily: 6 × 24 = 144 claims a day, i.e. 864 a week. Gap = 1,440 − 864 = 576 claims.
Three temporaries now fall short: 432 claims added, leaving a deficit of 144.
Option 1 - four temporaries. 4 × 24 × 6 = 576 claims, exactly closing the gap. Cost 4 × ₹4,200 = ₹16,800.
Option 2 - three temporaries plus maximum overtime. Six present clerks × 2 hours × 3 claims × 6 days = 216 extra claims, so 432 + 216 = 648, which covers the 576 gap. Cost = ₹12,600 + 72 hours × ₹210 = ₹12,600 + ₹15,120 = ₹27,720.
Option 3 - two temporaries plus overtime gives 288 + 216 = 504, which is 72 short and fails outright.
Judgement. Four temporaries is the cheapest route that clears the target without overtime, so the answer does change: the branch must move from three to four temporaries. The underlying principle is that temporary staff scale in units of 144 claims a week, while overtime scales in units of 216 across the whole team - overtime is a large, expensive block that is hard to match to a modest shortfall.