A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took 8 more days to finish the assignment. The value of m is equal to:

Solution

Maths sir · 4 steps

The total work in system-days is fixed, so the planned work equals the work done over 25 shrinking days.

1. Measure the work. Count work in system-days: one system working for one day is one unit. The plan was m systems for 17 days, so the assignment needs 17m system-days.
2. Systems each day. Day 1 has m systems, day 2 has m - 4, day 3 has m - 8, and so on. This is an AP with first term m and common difference -4. The job took 17 + 8 = 25 days, so add 25 terms.

   25/2[2m + (25-1)(-4)] = 17m

3. Solve. The left side is 25/2(2m - 96) = 25(m - 48) = 25m - 1200. So 25m - 1200 = 17m, which gives 8m = 1200 and m = 150.
4. So. m = 150. As a check, on day 25 there are still 150 - 96 = 54 systems running, so the setup makes sense. The answer is (c).

The idea to keep. When workers or machines drop off by a fixed number each day, the daily output forms an AP. Set its sum over the actual days equal to the planned total work.

Answer from the NTA final answer key. Solution by PrepWiser.