Question

Yogesh requires 3 days more than Vivek to do a work completely. If both

of them work together, the work can be completed in 2 days. Find the

number of days required for each of them to do the work completely.

Answer 1

here is your answer dear frnd

Answer 2

Answer:

Number of days required by Vivek = 3 days and

Number of days required by Yogesh = 6 days

Step-by-step explanation:

Let us suppose Vivek completes the work in ' x ' number of days

So,

Vivek's 1 day work = $\frac{1}{x}$

Yogesh requires 3 days more than Vivek to do a work completely

So,

Yogesh completes the work in ' x + 3 ' days'

Yogesh's 1 day work = $\frac{1}{x+3}$

When they are working together, work is completed in 2 days

Therefore,

$\frac{1}{x}$ + $\frac{1}{x+3}$ = $\frac{1}{2}$

$\frac{x+3+x}{x(x+3)}$ = $\frac{1}{2}$

$\frac{2x+3}{x^{2}+3x}$ = $\frac{1}{2}$

4x + 6 = x² + 3x

x² + 3x - 4x - 6 = 0

x² - x - 6 = 0

Solving for x:

x² - 3x + 2x - 6 = 0

x ( x - 3 ) + 2 ( x - 3) = 0

( x + 2 ) ( x - 3 ) = 0

x = - 2 or x = 3

Since, Number of days cannot be negative

x = 3

That is,

Vivek completes the work in 3 days

And Yogesh completes the work in x + 3 days = 3 + 3 = 6 days

Hence,

Number of days required by Vivek = 3 days and

Number of days required by Yogesh = 6 days