The sum of all 3 -digit numbers less than or equal to 500 , that are formed without using the digit 1 and they all are multiple of 11 , is ______.

Step-by-step solution

209 , 220 , 231 , . . . . . . . . , 495 series in A.P. Clearly, a = 209 ,   d = 220 - 209 = 11 and l = 495 Where a is the first term, d is the common difference and l is the last term. ⇒ l = a + n - 1 d = 495 where n is the number of terms ⇒ l = 209 + n - 1 11 = 495 ⇒ n - 1 11 = 286 ⇒ n - 1 = 26 ⇒ n = 27 Sum = 27 2 2 × 209 + 26 × 11 = 27 209 + 143 = 27 × 352 = 9504 Numbers containing 1 at unit place = 231 ,   341 ,   451 Numbers containing 1 at 10 th place