Multiple choice

$P$ is $30\%$ more efficient than $Q. P$ can complete a work in $23$ days. If $P$ and $Q$ work together, how much time will it take to complete the same work?

  1. 9

  2. 11

  3. 13

  4. 15
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P efficiency = 1.3 * Q efficiency. P takes 23 days, so total work = 23 * 1.3 = 29.9 units. Q takes 29.9 / 1 = 29.9 days. Combined rate = 1.3 + 1 = 2.3. Time = 29.9 / 2.3 = 13 days.

AI explanation

Let the efficiency of Q be 10 units per day, making P's efficiency 13 units per day. Since P completes the work alone in 23 days, the total work is 13 multiplied by 23, which equals 299 units. Working together, P and Q have a combined efficiency of 23 units per day. Dividing 299 by 23 gives exactly 13 days.

Keep practicing — related questions