If 4 men or 6 boys can finish a work in 20 days. How long will 6 men and 11 boys take to finish the same work?

If 4 men or 6 boys can finish a work in 20 days. How long will 6 men and 11 boys take to finish the same work?
1). 4 days
2). 5 days
3). 6 days
4). 7 days

4 men or 6 boys can complete the work in 20 days.

Work done by 4 men in 1 day = 1/20, so 1 man’s work = 1/(20×4) = 1/80.

Work done by 6 boys in 1 day = 1/20, so 1 boy’s work = 1/(20×6) = 1/120.

Work done by 6 men in 1 day = 6 × (1/80) = 3/40.

Work done by 11 boys in 1 day = 11 × (1/120) = 11/120.

Total work done in 1 day = (3/40) + (11/120) = 1/6.

Time required to finish the work = 1 ÷ (1/6) = 6 days.

Answer: 6 days (Option 3). 

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