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Painter A can paint a building in 12 days while Painter B can paint it in 16 days. If A and B work on alternate days, and A starts the work on the first day, then the number of days required to paint the building is

Solution

Correct Option: 1

Painter A can paint a building in 12 days while Painter B can paint it in 16 days.

So, let us assume the total work-done to be the LCM or some multiple of 12 and 16, let's take 192 (for simple calculation).

PersonAB
Rate1616 units/day1212 units/day
Time1212 days1616 days
Work-Done192192 units192192 units

A and B work on alternate days, with A starting first.

So, in every 2 days, work done is:

16+12=2816 + 12 = 28 units

In 12 days, there are 6 such pairs.

6×28=1686 \times 28 = 168 units

Work left:

192168=24192 - 168 = 24 units


Day 13 is A's turn.

A does 1616 units of work.

Work left after 13 days:

2416=824 - 16 = 8 units


Now B works on day 14.

B does 1212 units in 1 day.

So, time taken by B to complete 88 units is:

812=23\dfrac{8}{12} = \dfrac{2}{3} day


Total time required:

13+23=132313 + \dfrac{2}{3} = \boxed{13\dfrac{2}{3}} days

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