a + b can do a work in 6 days .a+b+C can do same work 5 days. a and c take 2.5 days less than b and c. then find the number of days taken by a, b and c individually complete work
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Solving for C -
1/A + 1/B +1/C=1/5 (Since A,B,C can together do work in 5 days)
1/A + 1/B = 1/6 (Since A and B can together do work in 6 days)
On solving,
C= (1/5) - (1/6)= 1/30 = 30 days
Let (B+C) complete the work in = x days
Let (A+C) complete the work in = x-2.5 days
Therefore,
= (1/A+B) + (1/B+C) + (1/C+A) = 2 × (1/A) + (1/B) + (1/C)
= (1/6) + (1/x) + (1/x-2.5) = 2/5
On simplifying -
= 47.5x - 75 + 5x² = 12x² - 30x
= 12x² - 5x² - 47.5x - 30x + 75 = 0
= 7x² - 77.5x + 75 = 0
= 7x (x-10) - 7.5x (x-10) = 0
Thus, x = 10
Therefore, (B + C) = 10 days, and (A + C) = 7.5 days
A = (1/5) - (1/10) = 1/10 = 10 days
B = (1/5) - (1/7.5) = 1/15 = 15 days
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