1 person works on a job on the first day, 2 persons work on the second day, 3 persons work on the third day and so on. The job gets completed by the end of 25 days. In how many days can the same job be completed if 25 persons working daily on it?
Correct Answer : b ) 13 daysExplanation :
According to question:
Let us assume efficiency of one person be 1 unit
As 1 person works on a job on the first day, 2 persons work on the second day, 3 persons work on the third day and so on till 25 days.
We know, Total work done = Efficiency × Time taken
⇒ Total unit of work done = 1 + 2 + 3.......... + 25
We know that, sum of first n numbers=\(n(n+1)\over2\)
⇒ Total unit of work done =\(25*(25+1)\over2\)=325 units
⇒ Total work = 325 units
As now only 25 men are working
⇒ 325 = 25 * days
⇒ Days = 13
Thus, the required number of days is 13 days
Hence, (b) is the correct answer.
Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA, UP SI etc.