Multiple choice

$A$ does half as much work as $B$ in one-sixth of the time. If together they take 10 days to complete a work, how much time shall $B$ alone take to do it?

  1. $70$ days
  2. $30$ days
  3. $40$ days
  4. $50$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A does half the work of B in 1/6 the time. If B takes T time for 1 unit, A takes (1/6)T time for 0.5 units. Thus, A's rate is 0.5 / (T/6) = 3/T. B's rate is 1/T. Combined rate: 3/T + 1/T = 4/T = 1/10. So T = 40.

AI explanation

Let us take the respective amounts of work done by A and B in one day as a and b. The statement implies A does half of B's work in a sixth of B's time, so a equals half divided by one sixth, which means a equals 3b. Since A and B together take 10 days, their combined daily work is a plus b equals one tenth. Substituting a equals 3b gives 4b equals one tenth, so b equals one fortieth. Therefore, B alone will complete the work in 40 days.

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