Question: 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-Solution:(2 × 14) men + (7 × 14) boys = (3 × 11) men + (8 × 11) boys⇒ 28 men + 98 boys = 33 men + 88 boys⇒ 5 men= 10 boys∴ 1man= 2 boysTherefore, (2 men + 7 boys) = (2 × 2 +7) boys = 11 boys(8 men + 6 boys) = (8 × 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)
Therefore, (22 × 1 × x) = (11 × 3 × 14)⇒ x = 21 Hence, the required number of days = 21