Mr Stanley employs a certain number of typists to type a project. After 8 days, 20 percent of the typists leave the job, and it is then found that the time required to complete the remaining work is equal to the time the entire work would have originally required with all the typists. The average typing speed of each typist is 20 pages per hour. What is the minimum possible number of typists that could have been originally employed?

Introduction / Context:
This question tests understanding of relative work rates and the effect of changing the number of workers during a job. We are told that some typists leave after a certain time, and yet the remaining work takes as long as the entire job would have taken with the original team. We must interpret this carefully and determine the smallest possible initial number of typists.

Given Data / Assumptions:
• Initial number of typists = N (to be found).
• All N typists together would take T days to finish the entire job.
• They actually work for 8 days with all N typists.
• After 8 days, 20 percent of the typists leave, so remaining typists = 0.8N.
• Time taken by the remaining typists to finish the rest of the work equals T days.
• Each typist types 20 pages per hour, but only relative rates matter.

Concept / Approach:
We consider work as a single unit. With N typists, total work equals N times T times their daily rate. Using equations for work done in the first 8 days and in the remaining period, we relate T to 8 and solve for T. The value of N is then restricted by the requirement that 20 percent of N is an integer and N itself is an integer. We choose the smallest such N as the answer.

Step-by-Step Solution:
Let the total work be W and daily work rate of each typist be r (in pages per day). If all N typists work for T days, total work W = N × r × T. In the first 8 days, work done = N × r × 8. Remaining work after 8 days = W − N × r × 8. After 8 days, number of typists = 0.8N, and they take T days to finish the remaining work. So remaining work = 0.8N × r × T. Equate the two expressions for remaining work: W − N × r × 8 = 0.8N × r × T. Substitute W = N × r × T: N × r × T − N × r × 8 = 0.8N × r × T. Divide both sides by N × r: T − 8 = 0.8T. Rearrange: T − 0.8T = 8, so 0.2T = 8, giving T = 40 days. To have 20 percent of N as an integer, N must be a multiple of 5. The minimum such integer is N = 5.

Verification / Alternative check:
With N = 5, total time with all typists would be T = 40 days. Work done in 8 days = 5 × r × 8 = 40r. Remaining work W − 40r = 5 × 40r − 40r = 160r. After 8 days, 20 percent of 5 is 1 typist, so 4 typists remain. Time taken by 4 typists to finish remaining work = 160r ÷ (4r) = 40 days, which matches T and satisfies the given condition.

Why Other Options Are Wrong:
Any smaller number than 5 would make 20 percent of N non integral, which is impossible for headcount. Larger multiples like 10 or 15 also satisfy the algebra but are not minimum, and the question explicitly asks for the minimum number of typists.

Common Pitfalls:
Many learners ignore the sentence about equal time for remaining work and original full work, or they misinterpret percentages of people as percentages of work. Another common error is to use the typing speed in pages per hour unnecessarily, which distracts from the main relationship between time and number of workers.

Final Answer:
The minimum number of typists originally employed is 5.