Multiple choice

$A$ can do a piece of work in $40$ days. He worked at it for $5$ days, then $B$ finished it in $21$ days. The number of days, that $A$ and $B$ take together to finish the work, are

  1. $15$ days
  2. $14$ days
  3. $13$ days
  4. $10$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A does 5/40 = 1/8 of the work. Remaining work = 7/8. B does 7/8 in 21 days, so B's rate is (7/8) / 21 = 1/24. Together, their rate is 1/40 + 1/24 = (3+5)/120 = 8/120 = 1/15. They take 15 days together.

AI explanation

Using the total work method, A's 5 days of work equals 5 divided by 40, which is 1/8 of the work. B completes the remaining 7/8 of the work in 21 days, meaning B's rate is (7/8) divided by 21, which simplifies to 1/24 of the work per day. A's daily rate is 1/40 and B's daily rate is 1/24; adding them together gives a combined daily rate of 1/15. Therefore, working together, they finish the entire work in 15 days.

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