Math, asked by Satvik2981, 1 month ago

In the six digit number 8()6()4(), the symbol () stands for the same digit. How many of the six digit numbers that can be formed by replacing () with a digit are divisible by 9 ?

Answers

Answered by sodialsarwar
0

Answer:

806040

836343

866646

896949

Step-by-step explanation:

8+0+6+0+4+0=18 is divisible by 9

8+3+6+3+4+3=27 is divisible by 9

8+6+6+6+4+6=36 is divisible by 9

8+9+6+9+4+9=45 is divisible by 9

Answered by RvChaudharY50
1

Solution :-

Let us assume that, () is denoted by x .

So, six digit number is 8x6x4x .

we know that,

  • When sum of all digits is divisible by 9 , the given number is also divisible by 9 .

then,

→ (8 + x + 6 + 4 + x) ÷ 9 = Remainder 0

→ (18 + 3x) ÷ 9 = Remainder 0

Putting value of x from 0 to 9 we get,

  • x = 0, => (18 + 3 * 0) = 18 ÷ 9 = Remainder 0 .
  • x = 1, => (18 + 3 * 1) = 21 ÷ 9 ≠ Remainder 0 .
  • x = 2, => (18 + 3 * 2) = 24 ÷ 9 ≠ Remainder 0 .
  • x = 3, => (18 + 3 * 3) = 27 ÷ 9 = Remainder 0 .
  • x = 4, => (18 + 3 * 4) = 30 ÷ 9 ≠ Remainder 0 .
  • x = 5, => (18 + 3 * 5) = 33 ÷ 9 ≠ Remainder 0 .
  • x = 6, => (18 + 3 * 6) = 36 ÷ 9 = Remainder 0 .
  • x = 7, => (18 + 3 * 7) = 39 ÷ 9 ≠ Remainder 0 .
  • x = 8, => (18 + 3 * 8) = 42 ÷ 9 ≠ Remainder 0 .
  • x = 9, => (18 + 3 * 9) = 45 ÷ 9 = Remainder 0 .

therefore, Possible values of x are ,

  • x = 0, 3, 6 and 9 .

hence, Possible Four six digits numbers are,

  • 806040
  • 836343
  • 866646
  • 896949

Total four six digit numbers can be formed by replacing () with a digit are divisible by 9 .

Learn more :-

if a nine digit number 260A4B596 is divisible by 33, Then find the number of possible values of A.

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