Mathematics · Linear Equations

On a construction project, three workers — Arjun, Bilal, and Chirag — were assigned three types of tasks: digging, cementing, and painting. Each spent the same number of hours on digging (x), cementing (y), and painting (z). The hours spent on each type of work were all distinct (x  =y  =z). The hourly wages for each worker for digging, cementing, and painting were given as follows: Arjun: Rs 12, Rs 8, Rs 5 (Total earned = Rs 260) Bilal: Rs 15, Rs 7, Rs 10 (Total earned = Rs 295) Chirag: Rs 10, Rs 9, Rs 6 (Total earned = Rs 225) Assertion (A): The hours spent by each worker on digging, cementing, and painting can be uniquely determined to be 10 hours, 10 hours, and 12 hours respectively. Reason (R): Framing and solving the system of three linear equations in terms of the hours worked will always yield a unique solution if the determinant of the coefficients is non-zero.