Question 18

# Arun and Amit can do a piece of work in 9 days and 12 days respectively. If they work for alternate days and Amit starts the work first, then in how many days 35/36 parts of whole work will be completed?

Solution

If A is working alone can finish his work in 9 days then his working efficiency will be $$\frac{1}{9}$$

Similarly work done by B in 12 days so his efficiency will be  $$\frac{1}{12}$$

Hence, Work done by A on day 1 is  $$\frac{1}{9}$$

and work done by B on day 2 is $$\frac{1}{12}$$. it means work done in first 2 days will be

( $$\frac{1}{9}$$ + $$\frac{1}{12}$$)=  $$\frac{7}{36}$$

Hence in 10 days total work done will be $$\frac{5\times 7}{36}$$ = 35/36.