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 = b2 – 6b
b2 – 14b + 24 = 0
Factorize b2 – 14b + 24 = 0
b2 – 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.