A factory is operating in two shifts, day and night, with 70 and 30 workers, respectively. If per day mean wage of the day shift workers is Rs. 54 and per day mean wage of all the workers is Rs. 60, then per day mean wage of the night shift workers (in Rs.) is:

We have two separate groups of workers. In the day-shift there are $$70$$ workers whose mean (average) wage per day is Rs.$$\,54$$. In the night-shift there are $$30$$ workers whose mean wage we have to find. Together these two groups form the whole factory work-force of $$70+30=100$$ workers, and the mean wage for the entire factory is given as Rs.$$\,60$$ per day.

The standard relation between mean, total wage, and number of workers is

$$\text{Mean wage} \;=\;\frac{\text{Total wage}}{\text{Number of workers}}.$$

First we compute the total wage paid to all the workers in one day. Using the overall mean, we write

$$\text{Total wage for all workers}= \text{Mean}_{\text{all}}\times\text{Number}_{\text{all}} = 60 \times 100 = 6000.$$

Now we find the total wage paid to only the day-shift workers. Using their mean of Rs.$$\,54$$, we have

$$\text{Total wage (day shift)}=\text{Mean}_{\text{day}}\times\text{Number}_{\text{day}} = 54 \times 70.$$

Carrying out the multiplication step by step:

$$54 \times 70 = (50+4)\times70 = 50\times70 + 4\times70 = 3500 + 280 = 3780.$$

The night-shift total wage is simply what remains when the day-shift wage is subtracted from the factory’s overall wage:

$$\text{Total wage (night shift)} = 6000 - 3780 = 2220.$$

Finally, to get the mean wage for the night-shift workers we again apply the mean formula, this time to the night-shift alone:

$$\text{Mean wage (night shift)} = \frac{\text{Total wage (night shift)}}{\text{Number (night shift)}} = \frac{2220}{30}.$$

We perform the division clearly:

$$2220\div30 = \frac{2220}{10}\div3 = 222\div3 = 74.$$

So, the per-day mean wage of the night-shift workers is Rs.$$\,74$$.

Hence, the correct answer is Option B.