Discussion
A can do a work in 14 days and B in 24 days. If they work on it together for 4 days, then the fraction of the work that is left is.
Answer: D
The fraction of the work left is 23/42. A does \(\frac{1}{14}\) of the work in a day and B does \(\frac{1}{24}\), so together they do \[ \frac{1}{14} + \frac{1}{24} = \frac{12 + 7}{168} \] \[ \frac{12 + 7}{168} = \frac{19}{168} \] In 4 days they do \(\frac{76}{168} = \frac{19}{42}\). The work left is \[ 1 - \frac{19}{42} = \frac{23}{42} \] The fraction 19/42 is the work done and not the work left, and the others, 18/42, 45/42 and 33/42, do not match.
Another way: take 168 units of work, the lcm of 14 and 24. A does 12 units and B 7 a day, so 4 days make 76 units, and 92 of 168 are left, which is 23/42.
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