Question

A takes 6 days less 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 alone?

Answer 1

Hope this solution will help :)

Answer 2

Answer:

Given:

• A takes 6 days less than B to do a work. If both A and B working together can do it in 4 days.

Find:

• How many days will B take to finish it alone?

Calculations:

• Let us assume x as the time taken by B to complete the work.

⇒ $\bold{\dfrac{1}{x} + \dfrac{1}{x} - 6 = \dfrac{1}{4}}$

⇒ $\bold{\dfrac{x-6+x}{x(x-6)}= \dfrac{1}{4}}$

⇒ $\bold{\dfrac{2x-6}{x^{2}-6x} = \dfrac{1}{4}}$

⇒ $\bold{8x-24 = x^{2}-6x}$

⇒ $\bold{x^{2}-14x+24 = 0}$

⇒ $\bold{(x^2-12x)+(-2x+24) = 0}$

⇒ $\bold{(x-12) , (x-2) = 0}$

⇒ ${\sf{\underline{\boxed{\red{\sf{x=12 }}}}}}$

Or

⇒ ${\sf{\underline{\boxed{\red{\sf{x=2 }}}}}}$