Final answer:
The difference between the wages of workers A and B is Rs.120, calculated based on their proportional contributions to the total work in comparison to the total wages of Rs.840.
Step-by-step explanation:
The subject of this question is the calculation of wages based on the proportion of work completed by two workers, A and B, who complete the work in 15 and 20 days respectively.
The total payment for the work completed is Rs.840.
To find the wage distribution, we calculate the daily work rate for both A and B by taking the reciprocal of the days they take to complete the work, giving us 1/15 and 1/20 as their respective daily work rates.
Combining the two gives us a daily work rate when both work together as 1/15 + 1/20 = 4/60 + 3/60 = 7/60.
To find the share of each worker, we first find the total work units completed by A and B, which are (1/15)/(7/60) for A and (1/20)/(7/60) for B.
These fractions yield 4/7 and 3/7 respectively, indicating the proportion of the total work done by A and B. We now multiply these proportions by the total wages, Rs.840, to get their individual wages: Rs.840 * (4/7) for A and Rs.840 * (3/7) for B.
Finally, to find the difference in wages between A and B, we subtract the smaller wage from the larger wage: (Rs.840 * (4/7)) - (Rs.840 * (3/7)) = Rs.840/7 = Rs.120.
Therefore, the difference in wages between A and B is Rs.120, which corresponds to option (c).