(a) Rs 7371
Given, Man : Woman : Child = 3 : 2 :1
\(\Rightarrow\) M = 3K , W = 2K, C = K, where K is a constant
\(\Rightarrow\) M = 3C , W = 2C
\(\therefore\) 20M + 30 W + 36C = 60C + 60C + 36C = 156C
and 15M + 21W + 30C = 45C + 42C + 30C = 117C
It is given that (20 men + 30 women + 36 children) = 156 children earn Rs 78 per day
\(\Rightarrow\) 1 child earns Rs \(\frac{78}{156}\) per day = Rs \(\frac{1}{2}\) per day.
\(\therefore\) (15 men + 21 women + 30 children) = 117
children should get \(\big(Rs\, \frac{1}{2}\times117\big)\) per day,
i.e., Rs \(\big(\frac{1}{2}\times117\times18\times7\big)\) = Rs 7371 in 18 weeks.