A and B together can do a certain work in x days. Working alone, A and B can do the same work in (x + 8) and (x + 18) days, respectively. A and B together will complete $\frac{5}{6}$ of the same work in:
Answer & explanation
Correct answer: option 3
A + B = x days,
A = (x + 8) days, ..(1)
B = (x + 18) days, ..(2)
⇒ Value of x will be under root of product of these 2 numbers =
√(8 + 18) = √144 = 12
⇒ x = 12.
Now putting value of x in (1) and (2),
⇒ A = (12 + 8) = 20 days
⇒ B = (12 + 18) = 30 days,
⇒ \(\frac{5}{6}\) of total work = \(\frac{5}{6}\) x 60 = 50 units.
⇒ Time taken by A + B to complete 50 units of work = \(\frac{50}{5}\) = 10 days. ..(\(\frac{Work}{Efficiency}\) = Time)