A group of persons can complete a piece of work in a certain time. If there were 4 more persons, they would take 2 days less to complete it. If there were 6 persons less, they would take 4 days more to complete it. What is the number of persons, initially, in the group?

Explanation

Given: If 4 Persons more then take 2 days less. And 6 Persons less, take 4 days more. Solution: Let person be n and days be x Total work = n × x According to Question, ⇒ n × x = (n + 4) (x - 2) --------------(1) ⇒ n × x = (n - 6) (x + 4) --------------(2) Solving Equation (1) and (2) we get, ⇒ 2n - 4x = -8 ⇒ 4x - 2n = 8 -----------------(3) ⇒ -4n + 6x = -24 ⇒ 2n - 3x = 12 ----------------(4) Adding Equation (3) and (4) We get, ⇒ 4x - 3x = 12 + 8 ⇒ x = 20 days Putting the value of x in equation (3) we get, ⇒ 80 - 2n = 8 ⇒ 2n = 72 ⇒ n = 72 / 2 ⇒ 36 Number of persons in Initially = 36