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2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the same in 11 days. Then, 8 men and 6 boys can do three times the amount of this work in

Correct Answer: 21 days

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)


  B o y s 22 : 11 W o r k 1   :   3   14 : x


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


=> x = 21 


Hence, the required number of days = 21


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