Multiple choice

Two workers A and B working together completed a job in $ 5$ days. If A worked twice as efficiently as he actually did and B worked $\displaystyle \frac{1}{3}$ as efficiently as he actually did the work would have been completed in $3$ days. A alone could complete the work in

  1. $\displaystyle 5\frac{1}{4}$ days
  2. $\displaystyle 6\frac{1}{4}$ days
  3. $\displaystyle 7\frac{1}{2}$ days

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

Let A and B alone complete the work in x and y days respectively, so their daily work sum is 1 over x plus 1 over y, which equals 1 over 5. The second condition gives the equation 2 over x plus 1 over 3y equals 1 over 3. Solving these equations by substituting 1 over x as a and 1 over y as b gives a equals 4 over 25 and b equals 1 over 25, meaning A alone takes 25 divided by 4 days, or 6 and one fourth days, to finish the work.

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