#### Question A takes 6 days lesser than B to do a work. If both A and B working together can do it in 4 days, how many days will B take to finish it?

#### Video Explanation

#### Explanatory Answer

Let A take ‘a’ days to finish the work.

Let B take ‘b’ days to finish the work.

A takes 6 days lesser than B to do a work **i.e., a = b – 6** ........... (1)

Together, they finish the work in 4 days. So, in one day they will complete \\frac{1}{4}) of the work.

In one day, A will complete \\frac{1}{a}) of the work.

In one day, B will complete \\frac{1}{b}) of the work.

Together they will complete ( \{\frac {1} {a}+\frac {1} {b}})) of the work in one day.

Therefore, \\frac{1}{a}) + \\frac{1}{b}) = \\frac{1}{4}) ........... (2)

Substitute (a = b – 6) in equation (2)

So, \\frac{1}{b - 6})+ \\frac{1}{b}) = \\frac{1}{4})

\\frac{b + b - 6}{(b - 6)b}) = \\frac{1}{4})

Cross multiplying the denominators we get 4(2b – 6) = (b – 6)b

8b – 24 = b^{2} – 6b

b^{2} – 14b + 24 = 0

Factorize b^{2} – 14b + 24 = 0

b^{2} – 12b – 2b + 24 = 0

(b – 12)(b – 2) = 0

Or b = 12 or b = 2

If b = 2, a = b – 6 = 2 – 6 = -4

Number of days cannot be negative. So, b cannot be 2.

The only value that b takes is 12. i.e., B takes 12 days to finish the work.