Question

3 men, 5 women and 7 children finish a job in 40 days; 6 men, 10 women and 18 children finish it in 18 days. In how many days can 9 men, 15 women and 5 children finish the same job?

• A. \(17\tfrac{17}{18}\)
• B. \(18\tfrac{18}{19}\)
• C. \(18\tfrac{17}{18}\)
• D. \(19\tfrac{18}{19}\)

Hint:

Look for a way to combine the two work-rate equations by scaling one of them so that the man and woman terms cancel out directly.

Answer 1

The Correct Option is B

Let one-day work be \(m,w,c\) and total work \(=1\). Then \(3m+5w+7c=\frac{1}{40}\) and \(6m+10w+18c=\frac{1}{18}\). Put \(x=3m+5w\): \(x+7c=\frac{1}{40}\) and \(2x+18c=\frac{1}{18}\Rightarrow x+9c=\frac{1}{36}\). Subtracting: \(2c=\frac{1}{36}-\frac{1}{40}=\frac{1}{360}\Rightarrow c=\frac{1}{720}\), and \(x=\frac{1}{40}-\frac{7}{720}=\frac{11}{720}\). Required group does \(9m+15w+5c=3x+5c=\frac{33}{720}+\frac{5}{720}=\frac{38}{720}=\frac{19}{360}\) per day. Time \(=\frac{360}{19}=18\tfrac{18}{19}\) days. Correct option: \(18\tfrac{18}{19}\).