The work done by a man, a woman and a child are in the ratio 3 : 2 : 1

1.	The work done by a man, a woman and a child are in the ratio 3 : 2 : 1. If the daily wages of 20 men, 30 women and 36 children amount to Rs 78, what will be the wages of 15 men, 21 women and 30 children for 18 weeks ? (a) Rs 7371 (b) Rs 8645 (c) Rs 9000 (d) Rs 9500
Answer» (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.

The work done by a man, a woman and a child are in the ratio 3 : 2 : 1. If the daily wages of 20 men, 30 women and 36 children amount to Rs 78, what will be the wages of 15 men, 21 women and 30 children for 18 weeks ? (a) Rs 7371 (b) Rs 8645 (c) Rs 9000 (d) Rs 9500

Answer»

(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.