Recovering a Typing Deadline After a Typist Falls Ill
A Hindi manuscript of 300 pages must be typed and delivered in five working days at the office of a District Sainik Welfare Board. Three typists are available. A types 20 pages a day at ₹20 a page and leaves about 1 error per page; B types 25 pages a day at ₹14 a page and leaves about 5 errors per page; C types 15 pages a day at ₹18 a page and leaves about 3 errors per page. Each typist works only one full shift a day, and the three speeds together exactly meet the deadline with no slack. Every error costs ₹5 to correct at the proof stage. On the morning of day 3, C reports sick and will not return. The clerk suggests giving all leftover work to B because B is cheapest per page; the officer wants the deadline held. You must compute the base plan cost, then choose the cheapest compliant recovery.
1. Compute the base cost of typing and proof correction under the original five-day plan.
Read the worked answer
- Pages over five days: A 20 × 5 = 100; B 25 × 5 = 125; C 15 × 5 = 75. Total = 300, so the plan exactly meets the manuscript size.
- Typing cost: 100 × 20 = ₹2,000; 125 × 14 = ₹1,750; 75 × 18 = ₹1,350. Total = ₹5,100.
- Errors: A 100 × 1 = 100; B 125 × 5 = 625; C 75 × 3 = 225. Total = 950 errors.
- Correction cost: 950 × 5 = ₹4,750.
- Base total: ₹5,100 + ₹4,750 = ₹9,850.
The important feature is that daily capacity equals daily requirement exactly (20 + 25 + 15 = 60 pages a day for 300 pages in five days). Any absence therefore creates an immediate arithmetic shortfall, not merely a delay.
2. At the start of day 3, how many pages are done and how many remain? Can A and B alone finish within the remaining three days?
Read the worked answer
- Work completed in two full days: A 40, B 50, C 30 = 120 pages.
- Remaining: 300 − 120 = 180 pages.
- Combined capacity of A and B: 20 + 25 = 45 pages a day.
- Capacity over the remaining three days: 45 × 3 = 135 pages.
- Shortfall: 180 − 135 = 45 pages.
So the deadline cannot be held by A and B on normal shifts. Exactly 45 pages must be produced outside the normal pattern - through overtime, a fourth typist, or an extension. This is the number that any recovery proposal must cover; a proposal that does not close the 45-page gap is not compliant with the officer's instruction.
3. The clerk says 'give the leftover work to B, B is cheapest per page'. Test that suggestion arithmetically, including correction cost, and recommend a recovery.
Read the worked answer
Both overtime options are priced at 1.5 times the normal page rate, and both must cover the same 45 pages.
Option B (clerk's suggestion): 45 × (14 × 1.5) = 45 × 21 = ₹945 typing. Errors: 45 × 5 = 225, correction 225 × 5 = ₹1,125. Total = ₹2,070.
Option A: 45 × (20 × 1.5) = 45 × 30 = ₹1,350 typing. Errors: 45 × 1 = 45, correction 45 × 5 = ₹225. Total = ₹1,575.
A is cheaper overall by ₹495, even though B is cheaper per page, because B's error rate is five times A's and the proof cost is charged per error. The clerk compared only the headline page rate, which is the wrong unit of comparison.
Recommendation: assign the 45-page overtime to A, subject to A's practical capacity (15 extra pages a day over three days). Record the comparison on file, since the cheaper-per-page option is the more expensive total option. If A cannot physically take 15 extra pages a day, split the overtime so that the marginal page goes to whichever typist has the lower all-in cost per page - A at ₹35 including correction, against B at ₹46.