Question

please answer ..........

Answer 1

Let the days required by Ajay to complete the work be (x+5), then days required by Vijay are x.

Let the total work be w.

Then,
Ajay's one day work =
$\frac{w}{x + 5}$
Vijay's one day work =
$\frac{w}{x}$
The total work done by them in one day=

$\frac{w}{x + 5} + \frac{w}{x} = \frac{w(2x + 5)}{ {x}^{2} + 5x }$
Their work done in 4 days =

$4 \times \frac{w(2x + 5)}{ {x}^{2} + 5x } = \frac{w(8x + 20)}{ {x}^{2} + 5x }$

This is the work done by them in 4 days. Now Vijay has left and only Ajay is left to work.

Remaining work which only Ajay has to do:

$w - \frac{w(8x + 20)}{ {x}^{2} + 5x} \\ = \frac{w( {x}^{2} - 3x - 20)}{ {x}^{2} + 5x }$

Now this is the work Ajay Does in 5 days.

Days taken by Ajay = Remaining work / Work done in 1 day.

Therefore,

$\frac{ \frac{w( {x}^{2} - 3x - 20)}{ {x}^{2} + 5x } }{ \frac{w}{x + 5} } = 5 \\ \frac{ {x}^{2} - 3x - 20}{x} = 5 \\ {x}^{2} - 3x - 20 = 5x \\ {x}^{2} - 8x - 20 = 0 \\ {x }^{2} - 10 x + 2x - 20 = 0 \\ (x - 10)(x + 2) = 0$
Since x is the number of days.

$x = 10$
The days required by Vijay to complete the work are 10.

The days required by Ajay to complete the work are (x+5) = 15.


Done.