Solution

Ashok can paint a house in six days. He works for eight days. That implies he painted 8/6 houses during this period. It means, he finished painting a house and painted a portion of the second house.

Baban took over from Ashok. Baban can paint a house in eight days, but he worked for six days. During this period, he could paint 6/8 houses.

So, the total work completed by Ashok and Baban = 8/6 + 6/8 = 100/48. It means they completed painting two houses and a little portion of the third house. Ashok worked for eights days, and Baban worked for six days, so they worked for fourteen days.

Chandra took up the work on the fifteenth day. He can paint a house in twelve days. Now, 100/48 houses have been painted, and there are three houses. So, the amount of unfinished work = 3 - 48/100 = 44/48. So, Chandra has to paint 44/48 houses. He can paint a house in twelve days, so, he will paint 44/48 houses in (44/48 × 12) = 11 days.

Praveen can thank his stars. Ashok worked for eight days, Baban worked for six days, and Chandra worked for eleven days. So, the work was completed in (8 + 6 + 11) = 25 days, three days ahead of the 28-day deadline.