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.
Answer & explanation
Correct answer: option 2
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