Time taken by Raju alone to complete the work = 15 days
Time taken by Priya alone to complete the work = Y days
When Priya joined Raju, total work is completed in (25/2) days
(12.5/15) + [(12.5-9)/Y] = 1
(3.5/Y) = 1 - (5/6)
(3.5/Y) = 1/6
Y = 21 days
time to complete work if they work together = (21*15) / (21+15) = 35/4 = 8 (3/4) days
Alternate Solution:
Let the Efficiency of Raju and Priya be X and Y respectively
According to the question-
Raju alone worked for the first 9 days and the remaining days 25/2 -9 = 7/2, they worked together
15*X = 9*X + (X+Y) *7/2
X/Y = 7/5
Total work = 15*7 = 105
Time to complete work if they work together = 105/12 = 8(3/4) days
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