Working together, A and B can do a certain work in 45

Solution

Let 'a', 'b' and 'c' is the working efficiency of A, B and C respectively. Let the total amount of work required = 90 units The time is taken by A and B to do a certain work = 45 days Therefore, The combined efficiency of A and B 90/ 45 = 2-unit a per day a + b = 2 The amount of work done by A and B in 10 days = 20 units the remaining work = 90-20 = 70 units The amount of work done A and B in the last 28 days [with C] = 56 units The amount of work done by C in 28 days = 70 - 56 = 14 units Therefore, The Efficiency of C =14/28 =1/2 Now, since the work done by C in 3 days is equal to the work done by B in 2 days, The amount of work done by C in 3 days = 3c units The amount of work done by C in 2 days = 2b units So, 3c =2b b =3c/2 =3/2×1/2 b=3/4. The efficiency of A =2-3/4 =5/4 Combined efficiency of A and C =1/2 +5/4 =7/4 The 70% of total work =90×70/100 =63. Taken time by A =63/ (7/4) = (63×4)/7 =252/7 =36days.