**Three men, A, B and C, worked together to paint a wall. If the painting was done by one man, the time taken to complete the wall for A, B and C would have been 6 hours, 8 hours and 12 hours respectively. A and B had painted for 3 hours after which A rested. B and C then continued with the painting. What would be the total number of hours taken to complete the wall? (Give your answer as a mixed number.)Solution**

First 3 hours

A painted for 3 h --> 3/6 = 1/2 (of the wall)*

B painted for 3 h --> 3/8 = 3/8 (of the wall)**

1/2 + 3/8 = 7/8 (of the wall was painted in first 3 hours)

* A takes 6h to paint the whole wall, therefore, in 3h, 3/6

** B takes 8h to paint the whole wall, therefore, in 3h, 3/8

A rests, B and C continue to paint remaining 1/8 of wall

Ratio of hours taken to paint whole wall

B : C

8 : 12

2 : 3

B takes less time than C, therefore B would have painted more of the wall

Ratio of amount of wall painted

B : C

3 : 2 --> Total units is 5

Time taken for B to paint whole wall

5/5 of wall --> 8h

Therefore, 3/5 of wall --> (3/5) x 8h = (24/5)h

Since only 1/8 of wall remains

1/8 of wall left --> (1/8) x (24/5)h = 3/5 h

Total time taken

--> 3h + 3/5 h = 3 and 3/5 hours

**Answer: 3 and 3/5 hours**

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