A takes 6 days less than time taken by B to finish the piece of work if both A - Maths - Quadratic Equations

Question

A takes 6 days less than time taken by B to finish the piece of
work if both A and B together can finish the work in 4 days find
the time taken by B to finish the work

Gursheen kaur. · Accepted Answer

Let B alone finish the work in x days Therefore, A alone can finish the work in (x â€“ 6) days $A's one day work = \frac{1}{(x - 6)} and B's one day work = \frac{1}{x}$ Given, (A + B) can finish the work in 4 days $∴ (A + B)'s one day's work = \frac{1}{4} \Rightarrow A' s one day work+ B's one day work = \frac{1}{4} \frac{1}{x - 6} + \frac{1}{x} = \frac{1}{4} \Rightarrow \frac{x + x - 6}{x (x - 6)} = \frac{1}{4} \Rightarrow \frac{2 x - 6}{x (x - 6)} = \frac{1}{4} \Rightarrow 4 (2 x - 6) = x (x - 6) \Rightarrow 8 x - 24 = x^{2} - 6 x \Rightarrow x^{2} - 6 x - 8 x + 24 = 0 x^{2} - 14 x + 24 = 0 x^{2} - 12 x - 2 x + 24 = 0 \Rightarrow x (x - 12) - 2 (x - 12) = 0 \Rightarrow (x - 12) (x - 2) = 0 \Rightarrow x = 12 or 2$ x â‰ 2, âˆµ if x = 2, then A alone can finish the work in = (2 â€“ 6) = â€“4 days, which is not possible âˆ´ x = 12, i e B alone can finish the work in 12 days and A alone will finish the work in 12 - 6 = 6 days

A takes 6 days less than time taken by B to finish the piece of work. if both A and B together can finish the work in 4 days find the time taken by B to finish the work