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Explanation:

(2 x 14) men +(7 x 14) boys = (3 x 11) men + (8 x 11) boys

=>5 men= 10 boys => 1man= 2 boys

Therefore, (2 men+ 7 boys) = (2 x 2 +7) boys = 11 boys

( 8 men + 6 boys) = (8 x 2 +6) boys = 22 boys.

Let the required number of days be x.

More boys , Less days (Indirect proportion)

More work , More days (Direct proportion)

Boys22:11Work1 : 3}⋮⋮ 14:x

Therefore, (22 * 1 * x) = (11 * 3 * 14)

=> x = 21

Hence, the required number of days = 21