A Review Note That Claims 55% and a Backlog of 205
The cyber cell of a Uttar Pradesh district recorded these figures: January 240 complaints received and 192 disposed; February 312 received and 234 disposed; March 390 received and 351 disposed. Pendency on 1 January was 40. In the monthly review the in-charge writes: "Complaints rose 30% in February and 25% in March, so the quarter's rise is 55%. Pendency is under control because March disposals were the highest ever." The cell has 8 operators and works 26 days a month, and disposal is counted only when the final report is filed. For April the SSP sets a target of bringing pendency down to 150 by 30 April, assuming April receipts repeat March's figure. The in-charge wants the operator to confirm his two statements in the review note and to say whether the April target is achievable with existing staff.
1. Check the 55% claim and state what can defensibly be written.
Read the worked answer
The two monthly figures are correct, the addition is not.
- January to February: 72 / 240 = 30.0%.
- February to March: 78 / 312 = 25.0%.
- January to March: 390 − 240 = 150, and 150 / 240 = 62.5%.
Check by compounding: 1.30 × 1.25 = 1.625, i.e. 62.5%, and 240 × 1.625 = 390. The arithmetic ties exactly.
Why 55% is wrong: the March rise is 25% of February's 312, not of January's 240. Percentages with different bases cannot be added. Adding them assumes the second rise is computed on the original base, which is precisely what did not happen.
Defensible sentence: "Receipts rose 30% in February and a further 25% in March, a cumulative rise of 62.5% over January."
Judgement: the error is small in direction but not in kind - it understates the rise by 7.5 percentage points in a document that will be quoted in the next review and in any staffing request. The operator should correct it before signature, with the calculation shown, rather than quietly editing the number.
2. Compute month-end pendency and disposal rates, and evaluate the statement that pendency is under control.
Read the worked answer
Pendency = opening + received − disposed.
- End January: 40 + 240 − 192 = 88
- End February: 88 + 312 − 234 = 166
- End March: 166 + 390 − 351 = 205
Disposal rate (disposed ÷ received):
- January: 192 / 240 = 80.0%
- February: 234 / 312 = 75.0%
- March: 351 / 390 = 90.0%
The statement is not supported. 351 is the highest absolute figure, but absolute disposals rise automatically when receipts rise - the number to watch is the ratio. In February the cell cleared only 75% of what came in and the backlog jumped by 78. Pendency rose in all three months, from 40 to 205, roughly fivefold.
Correct framing: "Disposals rose each month, and the March clearance rate improved to 90%, but receipts grew faster than capacity in February and pendency has risen every month to 205. Clearance rate and pendency must be read together." Highest-ever disposals alongside highest-ever backlog is not a contradiction; it is a capacity signal.
3. Is the April target (pendency down to 150) achievable with 8 operators in 26 working days? Show the arithmetic.
Read the worked answer
Required disposals = opening 205 + April receipts 390 − target 150 = 445.
Per working day: 445 / 26 = 17.12 complaints.
March's achieved rate: 351 / 26 = 13.50 per day.
Required productivity increase: 445 / 351 − 1 = 26.8%.
Per operator: March was 13.50 / 8 = 1.69 per operator per day. April needs 17.12 / 8 = 2.14 per operator per day.
In staffing terms: 17.12 per day at March's 1.69 each requires about 10.1 operator-equivalents - roughly 2 extra people, or the same 8 delivering 27% more.
Assessment: not achievable by exhortation. It needs one of: two additional hands on deputation or overtime; bulk disposal of a category that is not operator-bound (for example a batch of cases merely awaiting FSL reports, cleared in one sitting); or renegotiating the target to about 190 to 200, which matches March's demonstrated throughput.
Two cautions for the note: the 26.8% is a floor with no buffer - one day's shortfall carries forward and compounds. And the whole plan assumes April receipts equal March's; if receipts again rise 30% (to about 507), required disposals become 562, or 21.6 per day, and the plan fails outright. State the assumption explicitly rather than burying it.