The ratio of the amount of work done by (x+2) labours in 8 days and that done by (x-1) in 12 days is 4 : 3. Find the value of x.

25

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

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

⇒ \(\frac{(x + 2)\; \times\; 8}{(x - 1)\; \times\; 12}\) = \(\frac{W₂}{W₁}\)

We know, ratio of W₁ : W₂ = 4 : 3

⇒ \(\frac{(x + 2)\; \times\; 8}{(x - 1)\; \times\; 12}\) = \(\frac{3}{4}\)

⇒ 8(x + 2)    =  9 (x - 1) 

⇒ 9x - 8x     = 16 + 9

⇒    x = 25