A is twice as fast as B and B is one third as fast as C. If they together can complete a work in 30 days, in how many days can A, B and C individually do the same work?
Condition 1- A is twice as fast as B, means their ratio is 2 : 1. Condition 2- B is one third as fast as C, means their ratio is 1 : 3. Then we can say the ratio of A, B and C is as follows: According to condition 1: A : B = 2 : 1 According to condition 2 : B : C = 1 : 3 Thus, ratio of A : B : C = 2 : 1 : 3 This ratio denotes the working efficiencies of A, B and C, which means: A, B and C can do = (2 + 1 + 3 = 6) work/day Now, we can calculate the total work, i.e.: Total work = Total days × Per day work Total work = 30 × 6 = 180 A can do the same work in: = (Total work ÷ Efficiency of A) = 180 ÷ 2 = 90 days B can do the same work in: = (Total work ÷ Efficiency of B) = 180 ÷ 1 = 180 days C can do the same work in: = (Total work ÷ Efficiency of C) = 180 ÷ 3 = 60 days Thus, A, B and C can individually complete the same work in 90, 180 and 60 days, respectively.