Arpita and Nikita, working together, can complete an assigned job in 12 days. If Arpita works initially to complete 40% of the job, and the remaining job is completed by Nikita alone, then it takes 24 days to complete the job. The possible number of

Question

Arpita and Nikita, working together, can complete an assigned job in 12 days. If Arpita works initially to complete 40% of the job, and the remaining job is completed by Nikita alone, then it takes 24 days to complete the job. The possible number of days that Nikita requires to complete the entire job, working alone, is _________

Accepted Answer

Let Arpita's rate = 1/a, Nikita's = 1/n, with 1/a+1/n=1/12. Total work time when split: 0.4a+0.6n=24, i.e., 2a+3n=120. Solving the quadratic n2−44n+480=0 gives n=20 or n=24. Either is accepted.