The work done by (3x - 1) men in (2x + 3) days and the work done by (3x - 4) men in (2x + 1) days are in the ratio 4 : 3. Find the value of x.

Amount of work done by (3x - 1) men in (2x + 3) days = (3x - 1)(2x + 3),

Amount of work done by (3x - 4) men in (2x + 1) days = (3x - 4)(2x + 1)

According to question,

$\Rightarrow \dfrac{(3x - 1)(2x + 3)}{(3x - 4)(2x + 1)} = \dfrac{4}{3}$

3(3x − 1)(2x + 3) = 4(3x - 4)(2x + 1)

3(6x² + 9x − 2x − 3) = 4(6x² + 3x − 8x − 4)

3(6x² + 7x − 3) = 4(6x² − 5x − 4)

18x² + 21x − 9 = 24x² − 20x − 16

18x² − 24x² + 21x + 20x − 9 + 16 = 0

−6x² + 41x + 7 = 0

6x² − 41x − 7 = 0

6x² - 42x + x - 7 = 0

6x(x − 7) + 1(x − 7) = 0

(6x + 1)(x − 7) = 0

6x + 1 = 0 or x - 7 = 0

x = −$\dfrac{1}{6}$ or x = 7

x ≠ −$\dfrac{1}{6}$ as that will make number of men negative which is not possible.

Hence, value of x = 7.