Question

The time taken by a to complete the work is 4 days more than that taken by a and b together to complete the work and 5 more days than that taken by a and c together to complete the work. if efficiencies of b and c are in ratio 2:3 then a alone can do the work in

Answer 1

Productivity per day of a , b and c be equal to 1/a, 1/b and 1/c respectively. They can complete the given work (total) alone in a, b and c days respectively.

a and b can finish work together in ab/(a+b) number of days.

a and c can Together complete the work in ac/(a+c).

Given a = 4 + ab/ (a+b). -----(1)
a = 5 + ac/ (a+c). ----(2)
1/b : 1/c = 2 : 3.
So c = 2b/3 ----(3)
From (1), (3) & (2):

=> (a-4)(a-5) = 2b. ---(4)
=> (a-5)a = 2(a+b) ----(5)
Solving these we get
a = 10 days.
So b = 15.
And c = 10 days.

a and b can finish the work in 6 days. a & c can together complete the work in 5 days.