Five-Day Counter Load and the Staffing Note
In a Monday-to-Friday week the single-window counter of a branch in Vadodara logged three kinds of work: cash deposits, cash withdrawals, and 'other' (passbook, statement, KYC). The counts were: Monday 140 deposits, 96 withdrawals, 24 other; Tuesday 165, 105, 30; Wednesday 120, 88, 22; Thursday 180, 112, 28; Friday 210, 130, 40. The counter window runs 6.5 hours a day. Three clerks man the counter, and the branch work-study note puts the average time to complete one transaction at 2.5 minutes, including the customer's signing and cash-counting time. Saturday is a holiday and nothing is carried forward. The branch manager must send a staffing note covering the weekly average daily load, the day-on-day variation, and whether three clerks can absorb Friday's peak without overtime. The regional office has also asked at what average handling time Friday's load would stop fitting into the 6.5-hour window.
1. Compute the weekly average number of transactions per day and the share of cash deposits in the week's total.
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Daily totals (deposits + withdrawals + other):
- Mon: 140 + 96 + 24 = 260
- Tue: 165 + 105 + 30 = 300
- Wed: 120 + 88 + 22 = 230
- Thu: 180 + 112 + 28 = 320
- Fri: 210 + 130 + 40 = 380
Weekly total = 260 + 300 + 230 + 320 + 380 = 1,490. Average per working day = 1,490 / 5 = 298 transactions.
Deposit total = 140 + 165 + 120 + 180 + 210 = 815. Share = 815 / 1,490 = 0.5470, i.e. 54.7% (about 55 paise of every rupee of counter work is deposit work).
Cross-check: withdrawals 96 + 105 + 88 + 112 + 130 = 531, other = 144; 815 + 531 + 144 = 1,490, so no day has been double-counted. Deposits are the largest single block, which supports the note's recommendation to keep one dedicated deposit clerk.
2. By what percentage was Friday's total higher than Wednesday's, and what was the ratio of deposits to withdrawals on Friday?
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Percentage increase: use Wednesday as the base, since it is the earlier and lower figure. Increase = 380 − 230 = 150. Percentage = (150 / 230) × 100 = 65.217...%, i.e. about 65.2%.
Common error to avoid: dividing 150 by 380 (the Friday figure) gives 39.5%, which answers a different question - by what percentage Wednesday is below Friday.
Friday ratio: deposits 210, withdrawals 130. Divide both by 10 → 21 : 13. Check: 210/130 = 1.615 and 21/13 = 1.615, so the ratio holds. In percentage terms deposits were 210/380 = 55.3% of Friday's work and withdrawals 34.2%, leaving 10.5% for 'other'.
The 21:13 ratio matters for the note: cash outflow on the peak day is 130 withdrawals against 210 deposits, so the cash position stays surplus and no special currency chest indent is needed for Friday.
3. Can three clerks handle Friday's load inside the 6.5-hour window at 2.5 minutes per transaction? Also state the handling time at which the branch would just fail to clear Friday's load.
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Capacity available: 6.5 hours = 390 minutes. Three clerks give 3 × 390 = 1,170 clerk-minutes. At 2.5 minutes per transaction, capacity = 1,170 / 2.5 = 468 transactions.
Friday demand = 380 transactions. Utilisation = 380 / 468 = 0.8119, i.e. 81.2% - feasible, with slack of 468 − 380 = 88 transactions (about 220 clerk-minutes, or 3 hours 40 minutes of one clerk).
The 81% figure is high for a counter that also handles enquiries, so the note should recommend the peak-hour relief clerk rather than declaring the day comfortable.
Break point: the time at which Friday exactly fills the window is 1,170 / 380 = 3.079 minutes, i.e. about 3.08 minutes per transaction. Beyond 3.08 minutes the queue grows and the branch breaches closing time. Since 3.08 minutes is only 0.58 minutes above the current average, a small slip in handling time on the peak day wipes out the entire slack - that is the risk to put in the note.