Math, asked by tejasarjun82pabcwy, 1 year ago

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

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Answered by guptaramanand68
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.

tejasarjun82pabcwy: Thankyou..very.............much
guptaramanand68: You're welcome.
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