Multiple choice

A and B alone can do a piece of work in x and (x + 10) days respectively and they work together can finish the work in 9 3/8 days. Then find the efficiency ratio of A and B?

  1. 2:7

  2. 5:3

  3. 2:3

  4. 1:3

  5. 4:5

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

A takes x days, B takes x+10 days. Together they take 75/8 days. 1/x + 1/(x+10) = 8/75. (2x+10)/(x^2+10x) = 8/75. 150x + 750 = 8x^2 + 80x. 8x^2 - 70x - 750 = 0. 4x^2 - 35x - 375 = 0. Solving gives x = 15. A takes 15 days, B takes 25 days. Efficiency ratio is inverse of time ratio: 25:15 = 5:3.