The ratio of the amount of work done by (2x + 5) labours in 7 days and that done by (x - 1) in 10 days is 4 : 7. Find the value of x.

15

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

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

⇒ \(\frac{(2x + 5)\; \times\; 7}{(x - 1)\; \times\; 10}\) = \(\frac{W₂}{W₁}\)

We know, ratio of W₁ : W₂ = 4 : 7

⇒ \(\frac{(2x + 5)\; \times\; 7}{(x - 1)\; \times\; 10}\) = \(\frac{7}{4}\)

⇒ 4(2x + 5)    =   10(x - 1) 

⇒ 10x - 8x      =   30

⇒              x   = 15