Question

A takes 6 days less than the time taken by B to finish a piece of work. If both A and B work together they can finish in 4 days. Find the time taken by B to finish the work. 

Answer 1

Let B take 'c' days to finish the work. Hence, A will take 'c- 6' days. 

⇒ Work done by B in One day = `1/"c"` , whereas work done by A in one day = `1/("c" - 6)`

⇒ Work done by A and B combined in one day = `1/"c" + 1/("c" + 6) = ("c" - 6 + "c")/c`

Together they can complete the work in 4 days, hence: 

`("c"^2 - 6"c")/(2"c" - 6) = 4`

⇒ c² - 6c = 8c - 24 

⇒ c² -14c + 24 = 0 

⇒ c² -12c - 2c + 24 = 0 

⇒ c (c -12) - 2{c - 12) = 0 

⇒ (c -12) {c - 2) = 0. 

It can't be 2 as they together complete in 4 days and hence has to be more than that. 

Hence no. of days taken by B to finish the work = 12