Explanation

This is a man-days work problem: total work is proportional to (number of workers) × (number of days). The ratio condition gives (x + 2)(x − 3) : (x + 4)(x − 2) = 3 : 4, i.e. 4(x + 2)(x − 3) = 3(x + 4)(x − 2). Expanding: 4(x² − x − 6) = 3(x² + 2x − 8), so 4x² − 4x − 24 = 3x² + 6x − 24, which simplifies to x² − 10x = 0, i.e. x(x − 10) = 0. The root x = 0 would make the day counts negative and is inadmissible, leaving x = 10. Hence option (b). The distractors 8, 12, 15 do not balance the work ratio when substituted back.