Let the amount of work done in a day by,
- Men $= 6 \frac{units}{day}$
- Women $= 3 \frac{units}{day}$
- Child $= 1 \frac{unit}{day}$
Each person has a piar of hands. So, $39$ pairs of hands $39$ peoples.
The ratio of Men:Women:Child $= 6:5:2$
- The number of Men $= \frac{6}{13} \times 39 = 18$
- The number of Women $= \frac{5}{13} \times 39 = 15$
- The number of Children $= \frac{2}{13} \times 39 = 6$
Now, work done by,
- Men $= 108$ units
- Women $= 45$ units
- Child $= 6$ units
Total work done $= 159$ units
So, the wages of $6$ Children $= \frac{1113}{159} \times 6 = ₹42$
$\therefore$ The daily wages of a child $=\frac{42}{6} =₹7.$
Correct Answer $: \text{D}$