Question

vrujesh takes 6 days less to complete one work then Kaushal if Kaushal and vrujesh work together they can finish the work in 4 days in how many days Kaushal can alone finish the work ​

Answer 1

If both can together work in 4 days and Vrujesh takes 6 days less than Kaushal when wroking alone, then Kaushal can alone finish the work in 12 days.

Step-by-step explanation:

Let's assume that Kaushal alone takes "x" days to finish one work, then Vrujesh alone would finish the same work in "(x-6)" days.

So,

Work done by Kaushal in 1 day = $\frac{1}{x}$

Work done by Vrujesh in 1 day = $\frac{1}{(x-6)}$

It is also given that Kaushal and Vrujesh together can finish a work in 4 days

So, work done by Kaushal & Vrujesh together in 1-day = $\frac{1}{4}$

Now,  we can write the eq. as,

[Kaushal's one day's work] + [Vrujesh's one day's work] = [(Kaushal + Vrujesh)'s one day's work ]

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

⇒ $\frac{2x - 6}{x(x-6)} = \frac{1}{4}$

⇒ 8x - 24 = x² - 6x

⇒ x² - 14x + 24 = 0

⇒ x² - 12x - 2x + 24 = 0

⇒ x(x - 12) - 2(x - 12) = 0

⇒ (x - 12)(x - 2) = 0

⇒ x = 12 or 2

(If we take x = 2 days then Vrujesh will take 2-6 = -4 days, which is completely meaningless)

∴ x = 12 days

Thus, Kaushal can alone finish the work in 12 days.

-------------------------------------------------------------------------------------------

Also View:

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 ?

https://brainly.in/question/8587762

Manish takes 9 days more than his father to do a certain piece of work together they can do the work in 6 days •how many days will Manish take to do that work alone?

https://brainly.in/question/14532722

Answer 2

Answer:

hope u like it

Step-by-step explanation:

this is your answer....