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…
Question and options
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
- 20
- 24
- Both 20 and 24
- None of the given options is correct
Answer and explanation
Correct answer: C - Both 20 and 24
Let Nikita alone take y days; Arpita's rate = 1/12 - 1/y. Then 0.4/(1/12 - 1/y) + 0.6y = 24, giving y^2 - 44y + 480 = 0, so y = 20 or 24. Check: y = 20 gives Arpita 30 days, 12 + 12 = 24; y = 24 gives Arpita 24 days, 9.6 + 14.4 = 24. Both work, so the answer is both 20 and 24.
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IPMAT Indore
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