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.
Answer & explanation
Correct answer: option 3
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