Question : Amar can complete a work in 15 days and Prem in 12 days. Starting with Amar, they work on alternate days. In how many days will the work be completed?
Option 1: $13\frac{2}{5}$
Option 2: $12\frac{1}{6}$
Option 3: $13\frac{1}{2}$
Option 4: $13$
Correct Answer: $13\frac{2}{5}$
Solution :
Given: Time taken by Amar to complete work = 15 days
Time taken by Prem to complete work = 12 days
Starting with Amar, they work on alternate days.
Let the total work = LCM of 15 and 12 = 60 units
Amar’s 1 day work = $\frac{60}{15}$ = 4 units
Prem’s 1 day work = $\frac{60}{12}$ = 5 units
If they work on alternate days they will finish (4 + 5) = 9 units of work in 2 days,
In 12 days they will finish (9 × 6) = 54 units of work,
On the 13th day, Amar will finish 4 more units,
So, (54 + 4) = 58 units of work is done.
We have remaining (60 – 58) = 2 units of work, but Prem can finish 5 units in a day.
So, he will able to finish 2 units in $\frac{2}{5}$ day itself.
$\therefore$ Total work will be completed in $(13+\frac{2}{5})=13\frac{2}{5}$ days
Hence, the correct answer is $13\frac{2}{5}$.
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