If two persons A and B works 7 hours a day, then A and B alone can complete a piece of work in 6 days and 8 days respectively. While working 8 hours a day, in what time they would complete it together?
Q. If two persons A and B works 7 hours a day, then A and B alone can complete a piece of work in 6 days and 8 days respectively. While working 8 hours a day, in what time they would complete it together?
Answer: 3 days
Notes: A alone can complete the work in 42 days working 1 hour daily. Similiarly, B will take 56 days working 1 hour daily. A's 1 day's work $latex = \frac{1}{42}&s=1$ B's 1 day's work $latex = \frac{1}{56}&s=1$ (A + B)'s 1 day's work $latex = \frac{1}{42}+\frac{1}{56} = \frac{4+3}{168} = \frac{7}{168}&s=1$ ∴ Time taken by (A + B) working 8 hours daily $latex = \frac{168}{7\times 8} =&s=1$ 3 days Hence option [B] is correct answer.