A can do a piece of work in 14 days Which B can do in 21 days. they begin together but 3 days before the completion of the work, A leaves off. the total number of days to complete the work is:
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A takes 14 Days & B takes 21 Days. So, let the total work be LCM(14,21) = 42 Units
A -> 14 days = 3 Units/day
B -> 21 days = 2 Units/day
A + B = 5 Units/day
Now, for the last 3 days , only B worked as A left.
So, work done in the last three days = 2×3 = 6 units
Work done by A & B together = 42–6 = 36 units
Time taken = 365 = 7.2 days
Thus, TOTAL TIME = 3+7.2 = 10.2 Days (Answer) .
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Step-by-step explanation:
Let the total no. of days needed to complete the work be x days.
Let's assume total work to be 1.
- 1 day work of A = 1/14
- 1 day work of B = 1/21
Since A leaves 3 days before completion of work, therefore
- A works for (x-3) days.
- B works for x days.
ACCORDING TO QUESTION
(1/4) × (x-3) + (1/21) × x = 1
3x - 9 + 2x = 42
5x = 51
x = 10.2
So,Total days needed to complete the work = 10.2 days.
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