Question : Two persons A and B working separately can sanitise a building in 6 hours and 10 hours, respectively. They work in stretches of one hour alternately. If A begins at 8 a.m., then when will the work be finished?
Option 1: $9\frac{1}{3}$ h
Option 2: $7\frac{1}{3}$ h
Option 3: $6\frac{1}{3}$ h
Option 4: $8\frac{1}{3}$ h
Correct Answer: $7\frac{1}{3}$ h
Solution :
Person A can sanitise a building in 6 hrs.
Person B can sanitise a building in 10 hrs.
Total work = Efficiency$\times$Times
Let the total work = LCM of 6 and 10 = 30 units
Efficiency of A = $\frac{30}{6}$ = 5 units
Efficiency of B = $\frac{30}{10}$ = 3 units
According to the question,
(5+3) = 8 units of work done in 2 hours
So, in 6 hours work done = $8\times\frac{6}{2} = 24$ units
Till 7th hour, work completed = 24 + 5 = 29 units
Remaining work = 30 – 29 = 1 unit
1 unit of work is completed by B in $\frac{1}{3}\ \mathrm{hour}$
Total time is taken to complete the total work = $7\frac{1}{3}$ h
Hence, the correct answer is $7\frac{1}{3}$ h.
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