Multiple choice

$A$ alone can do a piece of work in $15$ days to that of $B$ alone can do it in $10$ days. If $B$ works at it for $5$ days and then leaves, then $A$ alone can finish the remaining work in _________.

  1. $6\dfrac {1}{2} days$
  2. $7\dfrac {1}{2} days$
  3. $8\ days$
  4. $6\ days$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate = 1/15, B's rate = 1/10. B works for 5 days: 5 * (1/10) = 1/2 work done. Remaining work = 1/2. A finishes 1/2 work at rate 1/15: (1/2) / (1/15) = 15/2 = 7.5 days.

AI explanation

Using the least common multiple method, assume the total work is 30 units. A's rate is 30 divided by 15, which is 2 units per day, and B's rate is 30 divided by 10, which is 3 units per day. B works for 5 days to complete 5 multiplied by 3, equaling 15 units, leaving 15 units of work. A can finish the remaining 15 units at a rate of 2 units per day, which takes 15 divided by 2, resulting in 7 and 1/2 days.

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