Question

the work done by 2x-3 men in 3x+1 days and tge work done by 3x+1 men in x+8 days are in ratio 11:15, fin ths valu of x

Answer 1

Answer:

The value of x is 7

Step-by-step explanation:

Given as :

The work done by 2 x - 3 men , in 3 x + 1 days

And , The work done by 3 x + 1 men , in x + 8 days are in ratio 11 : 15

According to question

$\dfrac{men \times days}{work}$   =  constant

Or, $\dfrac{(2x - 3)(3x+1)}{(3x+1)(x+8)}$   =  $\dfrac{11}{15}$

Or, $\dfrac{6x^{2} +2x-9x-3}{3x^{2} +24x+x+8}$  = $\dfrac{11}{15}$

Or, $\dfrac{6x^{2} -7x-3}{3x^{2} +25x+8}$   = $\dfrac{11}{15}$

Or, 15 ( 6 x² - 7 x - 3) = 11 ( 3 x² + 25 x + 8)

Or, 90 x² - 105 x - 45 = 33 x² + 275 x + 88

Or, 90 x² - 105 x - 45 - 33 x² - 275 x - 88 = 0

or, 57 x² - 380 x - 133 = 0

Now, Solving this quadratic equation

 x = $\dfrac{57\pm \sqrt{(-57)^{2}-4\times 57\times (-133))}}{2\times 57}$

∴  x = 7 ,  - 0.33

So, The value of x = 7

Hence, The value of x is 7 Answer