Question : In a factory, Ajay and Vijay work on the same machine to cut diamonds but on an alternate-hour basis. Ajay works for the first hour and then Vijay works for the second hour and so on. Ajay can complete the work in 6 hours, while Vijay completes it in 16 hours if they work individually. In how much time can they complete the work if they are using the machine on an alternate basis?
Option 1: 8 hr 30 min
Option 2: 8 hr
Option 3: 9 hr
Option 4: 9 hr 30 min
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Correct Answer: 8 hr 30 min
Solution :
Time taken by Ajay to complete the work = 6 hours
⇒ Part of work done by Ajay in an hour = $\frac{1}{6}$
Time taken by Vijay to complete the work = 16 hours
⇒ Part of work done by Vijay in an hour = $\frac{1}{16}$
Work done by first 2 hours = $\frac{1}{6}$ + $\frac{1}{16}$ = $\frac{8+3}{48}$ = $\frac{11}{48}$
Work done by (2 × 4) i.e. 8 hours = $\frac{11×4}{48}$ = $\frac{44}{48}$
Remaining work = $\frac{48-44}{48}$ = $\frac{4}{48}$
Time taken by Ajay to complete the remaining work
= $\frac{\frac{4}{48}}{\frac{1}{6}}$ = $\frac{4×6}{48}$ = $\frac{1}{2}$ hr = 30 min
So, the total time taken = 8 hr 30 min
Hence, the correct answer is 8 hr 30 min.
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