Question : If 4 men or 6 boys can finish a piece of work in 20 days, then in how many days can 6 men and 11 boys finish the same work?
Option 1: 5
Option 2: 6
Option 3: 7
Option 4: 8
Correct Answer: 6
Solution :
Time taken by 4 men to complete the work = 20 days
Part of work done by 4 men in a day = $\frac{1}{20}$
Part of work done by 1 man in a day = $\frac{1}{20×4}=\frac{1}{80}$
Time taken by 6 boys to complete the work = 20 days
Part of work done by 6 boys in a day = $\frac{1}{20}$
Part of work done by 1 boy in a day = $\frac{1}{20×6}=\frac{1}{120}$
Part of the work done by 6 men and 11 boys in a day
= $\frac{6}{80} + \frac{11}{120}$
= $\frac{3}{40} + \frac{11}{120}$
= $\frac{9+11}{120}$
= $\frac{1}{6}$
Time taken by 6 men and 11 boys to complete the work
= 6 days
Hence, the correct answer is 6.
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