Given: The average of a group of numbers is 64. When a number is added to the group, the average becomes 70. When the number is again added to the group, the average is again increased to 75. Assumption: Let there be ‘n’ numbers in the group and the number to be added be ‘x’ Calculation: Sum of numbers in group = 64n When x is added to the group, sum of numbers in group = 70(n + 1) ⇒ 64n + x = 70(n + 1) ⇒ x = 70n + 70 – 64n ⇒ x = 6n + 70 .... (1) Now, when x is again added, sum of numbers in group = 75(n + 2) ⇒ 70(n + 1) + x = 75(n + 2) ⇒ 70n + 70 + x = 75n + 150 ⇒ x = 5n + 80 .... (2) Equating (1) and (2), ⇒ 6n + 70 = 5n + 80 ⇒ 6n – 5n = 80 – 70 ⇒ n = 10 Substituting in eq. (1), ⇒ x = 6(10) + 70 ⇒ x = 60 + 70 = 130 ∴ The number is 130