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
18 days
21 days
24 days
30 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)
Boys22:11Work1 : 3}⋮⋮ 14:x
Therefore, (22 * 1 * x) = (11 * 3 * 14)
=> x = 21
Hence, the required number of days = 21