Multiple choice

Choose the correct answer from the alternatives given : Working together A and B can finish a piece of work in 5 days. If working speed of A was doubled and working speed of B reduced to half the same work was done in 4 days. In how many days can A finish the work alone.

  1. $10$ days
  2. $12$ days
  3. $15$ days
  4. $8$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A and B's rates be a and b. 1/a + 1/b = 1/5. If A is 2a and B is b/2, 1/(2a) + 1/(b/2) = 1/4, which is 1/(2a) + 2/b = 1/4. Solving the system: 1/a + 1/b = 1/5 and 1/(2a) + 2/b = 1/4. Multiply first by 2: 2/a + 2/b = 2/5. Subtract second: 1.5/a = 2/5 - 1/4 = 3/20. So 1/a = (3/20) * (2/3) = 1/10. A takes 10 days.

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