Question

If Yash works alone he would take 4 days more to complete the job than if both Yash and Kush worked
together. If Kush works alone, he would take 9 days more to complete the job than they work together.
How many days would they take to complete the work if both of them worked together?​

Answer 1

It would take them 6 days to complete the work together.

Given:

If Yash works alone he would take 4 days more to complete the job than if both Yash and Kush worked together. If Kush works alone, he would take 9 days more to complete the job than they work together.

To Find:

How many days would they take to complete the work if both of them worked together?​

Solution:

Let Yash and Kush together complete the work in x days.

Therefore, Time taken by Yash = (x+4) days

Time taken by Kush= (x+9) days

$\frac{1}{x+4}$ +$\frac{1}{x+9}$ = $\frac{1}{x}$

$\frac{x+9+x+4}{(x+4)(x+9)}$ = $\frac{1}{x}$

 $\frac{2x+13}{x^2+13x+36} = 1/x$

$2x^{2} + 13x = x^2+13x+36$

$x^{2} = 36\\x = \sqrt{36} \\x=6 days$

Therefore, it would take them 6 days to complete the work together.

Answer 2

The number of days would they take to complete the work if both of them worked together is 36 days.

Given:

Yash works alone he would take 4 days more to complete the job than if both Yash and Kush worked together. If Kush works alone, he would take 9 days more to complete the job than if they worked together.

To Find:

The number of days would they take to complete the work if both of them worked together.

Solution:

To find the number of days would they take to complete the work if both of them worked together we will follow the following steps:

As given in the question:

Let the Yash and kush take x days to complete the work together.

Now,

As given in the question:

Time taken by the Yash in working alone is 4 times more than working together.

So,

Time is taken by Yash in working alone = x + 4

Also,

Time is taken by kush in working alone = x + 9

Now,

Forming the equation we get,

$\frac{1}{x + 4} + \frac{1}{x + 9} = \frac{1}{x}$

$\frac{(x + 9) + (x + 4)}{(x + 9)(x + 4)} = \frac{1}{x}$

$\frac{2x + 13}{ {x}^{2} + 13x + 36 } = \frac{1}{x}$

$2 {x}^{2} + 13x = {x}^{2} + 13x + 36$

2x² - x² = 36

x² = 36

$x = \sqrt{36} = 6$

Henceforth, the number of days would they take to complete the work if both of them worked together is 36 days.

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