The ratio of the amount of work done by (x-1) labours in 5 days and that done by (x + 2) in 6 days is 2 : 3 . Find the value of x.

13

Formula used =\(\frac{Men\; \times\; Days}{Work}\) = Constant

Thus, \(\frac{M₁\; \times\; D₁}{M₂\; \times\; D₂}\) = \(\frac{W1}{W2}\)

⇒ \(\frac{(x - 1)\; \times\; 5}{(x + 2)\; \times\; 6}\) = \(\frac{W1}{W2}\)

We know, ratio of W₁ : W₂ = 2 : 3

⇒ \(\frac{(x - 1)\; \times\; 5}{(x + 2)\; \times\; 6}\) = \(\frac{2}{3}\)

⇒ 15(x - 1)    =   12(x + 2) 

⇒ 15x - 12x   = 24 + 15

⇒       3x       =  39            ⇒  x = 13