Question

E-3.
A four digit number plate of car is said to be lucky if sum of first two digit is equal to sum of last two
digit. Then find the total number of such lucky plate. (Assume 0000.0011.0111. ........ all are four digit
number)​

Answer 1

Answer:

670

Step-by-step explanation:

Let the 4 digits of car be L M N O

Case 1) L + M = N + O = 0 -  LM,NO - 00 , Number possible 1

Case 2) L + M = N + O = 1 -  LM,NO - 01, 10 , Number possible 2 x 2 = 4

Case 3) L + M = N + O = 2 - LM,NO - 20,02,11 , Number possible 3 x 3 = 9

Case 4) L + M = N + O = 3 - LM,NO - 30,12,03,21 , Number possible 4 x 4 = 16

Case 5) L + M = N + O = 4 - LM,NO - 40,13,04,31.22 , Number possible 5 x 5 = 25

Case 6) L + M = N + O = 5, Number possible 6 x 6 = 36

Case 7) L + M = N + O = 6, Number possible 7 x 7 = 49

Case 8) L + M = N + O = 7, Number possible 8 x 8 = 64

Case 9) L + M = N + O = 8, Number possible 9 x 9 = 81

Case 10) L + M = N + O = 9, Number possible 10 x 10 = 100

Case 11) L + M = N + O = 10, LM,NO - 55, 64,46, 73,37, 28,82, 19,91 Number possible 9 x 9 = 81

Case 12) L + M = N + O = 11, LM,NO - 56, 65,47, 74,38, 83,92, 92 Number possible 8 x 8 = 64

Case 13) L + M = N + O = 12,  Number possible 7 x 7 = 49

Case 14) L + M = N + O = 13,  Number possible 6 x 6 = 36

Case 15) L + M = N + O = 14,  Number possible 5 x 5 = 25

Case 16) L + M = N + O = 15,  Number possible 4 x 4 = 16

Case 17) L + M = N + O = 16,  Number possible 3 x 3 = 9

Case 18) L + M = N + O = 17,  Number possible 2 x 2 = 4

Case 19) L + M = N + O = 18,  Number possible 1 x 1 = 1

So Sum up we have =  1 + 4+ 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 + 81 + 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1

So Sum up we have = 670 lucky plates