B and C together takes 33.33% more time as compared to the time taken by A, B, C working together to finish a piece of work. C gets Rs. 700 out of the Rs.1750 they get in total as pay. In how many days C alone will finish the work if A, B takes 24 day more than all working together?
Answers
Given : B and C together takes 33.33% more time as compared to the time taken by A, B, C working together to finish a piece of work. C gets Rs. 700 out of the Rs.1750 they get in total as pay
To Find : In how many days C alone will finish the work if A, B takes 24 day more than all working together
Solution:
Let say A , B & C finish work together in 3D Days
then A & B Complete Work in 3D + 24 Days
B and C together takes 33.33% more days = 3D + D = 4D
1/A + 1/B + 1/C = 1/3D
1/A + 1/B = 1/(3D + 24)
1/B + 1/C = 1/4D
1/A = (1/A + 1/B + 1/C ) - (1/B + 1/C) = 1/3D - 1/4D = 1/12D
1/C = 1/3D - 1/(3D + 24) = ((D + 8) - D )/3D(D + 8) = 8/3D(D +8)
(8/3D(D + 8))/(1/3D) = 700/1750
=> 8/(D + 8) = 2/5
=> 40 = 2D + 16
=> D = 12
1/C = 8/3*12(12 + 8)
=> C = 90
C alone will finish the work in 90 Days
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