7 does not occur in 1000. So we have to count the number of times it appears between 1 and 999. Any number between 1 and 999 can be expressed in the form of xyz where 0 < x, y, z < 9.
Choose the correct option.
A) 200
B) 300
C) 400
D) 500
E) 470
1. The numbers in which 7 occurs only once. e.g 7, 17, 78, 217, 743 etc   This means that 7 is one of the digits and the remaining two digits will be any of the other 9 digits (i.e 0 to 9 with the exception of 7)   You have 1*9*9= 
<gadget id="calculator">1*9*9</gadget>
<output>81</output>
81 such numbers. However, 7 could appear as the first or the second or the third digit. Therefore, there will be 3*81= 
<gadget id="calculator">3*81</gadget>
<output>243</output>
243 numbers (1-digit, 2-digits and 3- digits) in which 7 will appear only once.   In each of these numbers, 7 is written once. Therefore, 243 times.   2. The numbers in which 7 will appear twice. e.g 772 or 377 or 747 or 77   In these numbers, one of the digits is not 7 and it can be any of the 9 digits ( 0 to 9 with the exception of 7).   There will be 9 such numbers. However, this digit which is not 7 can appear in the first or second or the third place. So there are   3 * 9= 
<gadget id="calculator">  3 * 9</gadget>
<output>27</output>
27 such numbers.   In each of these 27 numbers, the digit 7 is written twice. Therefore, 7 is written 54 times.   3. The number in which 7 appears thrice - 777 - 1 number. 7 is written thrice in it.   Therefore, the total number of times the digit 7 is written between 1 and 999 is  243 + 54 + 3= 
<gadget id="calculator"> 243 + 54 + 3</gadget>
<output>300</output>
300   Option 300
<result>B</result>
7 does not occur in 1000. So we have to count the number of times it appears between 1 and 999. Any number between 1 and 999 can be expressed in the form of xyz where 0 < x, y, z < 9.