Question

A and b working together can do a work in 6 days. if a takes 5 days less than b to finish the work, in how many days b alone can do the work ?

Answer 1

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Let the work done in one day be 'a' and 'b' respectively,

$1/a + 1/b = 1/6$

$\frac{1}{b-5} + \frac{1}{b} = \frac{1}{6}$

$\frac{b+b-5}{b^2 - 5b} = \frac{1}{6}$

$\frac{2b - 5}{b^2 - 5b} = \frac{1}{6}$

$b^2 - 5b = 12b - 30$

$b^2 - 5b - 12b + 30 = 0$

$b^2 - 17b + 30 = 0$

By solving qudratic equation,

$b = 2, b = 15$