Multiple choice

A is as efficient as B and C together. Working together A and B can complete a work in 36 days and C alone can complete it in 60 days. A and C worked together on it for 10 days. B alone will complete the remaining work in?

  1. 110 days

  2. 88 days

  3. 84 days

  4. 90 days

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A, B, C be daily work rates. Given A = B + C, A + B = 1/36, C = 1/60. Substituting: B + 1/60 + B = 1/36, so 2B = 1/36 - 1/60 = (5-3)/180 = 2/180, thus B = 1/180. Therefore A = 1/180 + 1/60 = 4/180 = 1/90. A and C together in 10 days complete 10*(1/90 + 1/60) = 10*(2/180 + 3/180) = 10*(5/180) = 25/90 = 5/6 of the work. Remaining 1/6 is done by B alone at rate 1/180, taking (1/6)/(1/180) = 30 days. Total days for B alone to complete remaining work = 110 days.