Question : Ravi can do a piece of work in 40 days and Sudha can do the same piece of work in 60 days. If they work on alternative days, starting with Sudha on the first day, then in how many days will the work be completed?
Option 1: 40
Option 2: 60
Option 3: 48
Option 4: 45
Correct Answer: 48
Solution :
Ravi can do a piece of work in = 40 days
Sudha can do the same piece of work in = 60 days
Sudha can finish the work per day = $\frac{1}{60}$
Ravi can finish the work per day = $\frac{1}{40}$
Ravi and Sudha can complete the work in one pair of days $= \frac{1}{60}+\frac{1}{40} = \frac{2+3}{120} = \frac{5}{120} = \frac{1}{24}$
They complete the work in 24 pairs of days.
$\therefore$ Ravi and Sudha can complete the work in 48 days.
Hence the correct answer is 48.
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