Question : A and B alone can do a piece of work in 4 and 9 days, respectively. In how many days will the work be completed, if they both work on alternate days, starting with B?
Option 1: $5\frac{1}{3}$
Option 2: $5\frac{2}{3}$
Option 3: $5$
Option 4: $5\frac{1}{4}$
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Correct Answer: $5\frac{2}{3}$
Solution :
Given: Time taken by A to complete the work = 4 days
Time taken by B to complete the work = 9 days
They both work on alternate days, starting with B.
Let the total work = LCM of 4 and 9 = 36 units
A’s 1 day's work = $\frac{36}{4}$ = 9 units
B’s 1 day's work = $\frac{36}{9}$ = 4 units
If they work on alternate days they will finish (4 + 9) = 13 units of work in 2 days,
In 4 days they will finish (13 × 2) = 26 units of work,
On the 5th day, B will finish 4 more units,
So, (26 + 4) = 30 units of work is done.
We have remaining (36 – 30) = 6 units of work, but A can finish 9 units in a day.
So, he will able to finish 6 units in $\frac{6}{9}=\frac{2}{3}$ day itself.
$\therefore$ Total work will be completed in $(5+\frac{2}{3})=5\frac{2}{3}$ days
Hence, the correct answer is $5\frac{2}{3}$.
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