A man and a boy together can do a certain amount of digging in 28 days. Their speeds in digging are in the ratio of 7 : 4. How many days will the boy take to complete the work if engaged alone?

Question: A man and a boy together can do a certain amount of digging in 28 days. Their speeds in digging are in the ratio of 7 : 4. How many days will the boy take to complete the work if engaged alone?Solution:Ratio of digging speeds of man and boy = 7 : 4Ratio of times taken by man and boy = 4 : 7Suppose the man takes 4x days while the boy takes 7x∴ Man's 1 day's work = 1/4x part ∴ Boy's 1 day's work = 1/7x partATQ,1/4x + 1/7x = 1/28⇒ (7 + 4)/28x = 1/28⇒ 11/28x = 1/28⇒ 28x = 28 × 11∴ x = 11Hence, time taken by the boy to complete the work alone = (7 × 11) days = 77 days