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Pramod can paint a wall red in 12 hours while Brajen can paint the wall red completely in 16 hours. If Pramod and Brajen work alternately for an hour each stalling when the wall has just cement on it till when it is completely painted red, how many hours will it take to paint the entire wall red?

Pramod can paint a wall red in 12 hours while Brajen can paint the wall red completely in 16 hours. If Pramod and Brajen work alternately for an hour each stalling when the wall has just cement on it till when it is completely painted red, how many hours will it take to paint the entire wall red? Correct Answer 13 hours 40 minutes

Pramod can paint a wall red in 12 hours while Brajen can paint the wall red completely in 16 hours

So, total work (LCM of 12 and 16) = 48 units

Pramod can paint the wall in 1 hour = 48/12 = 4 unit

Brajen can paint the wall in 1 hour = 48/16 = 3 unit

If Pramod and Brajen work alternately for an hour

So, work done in 2 hours = 7 units

Work done in 12 hours = 7 × 6 = 42 units

Now, Work done by Pramod in next 1 hour = 42 + 4 = 46 units

Remaining work = 48 - 46 = 2 units

Now, 3 units’ work done by Brajen = 1 hours

Thus, 2 units’ work done by Brajen = 1/3 × 2 hours = 2/3 hours = 2/3 × 60 = 40 min

∴ Total time = 12 + 1 + 2/3 = 13 hours 40 minutes

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