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# If 148101B095 is divisible by 33, find the value of B.

**Solution**

If the __number__ is divisible by 33 it has to be divisible by 11 and 3.

For the number to be divisible by 3 the __sum__ of its digits should be divisible by 3

1 + 4 + 8 + 1 + 0 + 1+ B + 0 + 9 + 5 = 29 + B

B should be atleast 1 to make 29 + B divisible by 3

For the number to be divisible by 11 the difference of the sum of digits in odd places and sum of digits in even places is either 0 or 11

(1 + 8 + 0 + B + 9) - (4 + 1 + 1 + 0 + 5) = 0

18 + B - 11 = 0

B = - 7

(1 + 8 + 0 + B + 9) - (4 + 1 + 1 + 0 + 5) = 11

18 + B - 11 = 11

B = 4

If B = 4 then sum of digits becomes 33 and that is divisible by 3.

So if B = 4 it becomes divisible by 33

**✦ Try This: I**f 679B328321 is divisible by 99, find the value of B.

If the number is divisible by 99 it has to be divisible by 11 and 9.

For the number to be divisible by 9 the sum of its digits should be divisible by 9

6 + 7 + 9 + B + 3 + 2 + 8 + 3 + 2 + 1 = 41 + B

B should be atleast 4 to make 41 + B divisible by 9. Next value of B is 13 but that is not single digit.

For the number to be divisible by 11 the difference of the sum of digits in odd places and sum of digits in even places is either 0 or 11

(6 + 9 + 3 + 8 + 2 ) - (7 + B + 2 + 3 + 1) = 0

25 - B - 13 = 0

B = 12

Which is not valid value of B because it is two digits.

(6 + 9 + 3 + 8 + 2) - (7 + B + 2 + 3 + 1) = 11

28 - B - 13 = 11

B = 4

If B = 4 the number 679B328321 becomes divisible by 99.

**☛ Also Check: **NCERT Solutions for Class 8 Maths Chapter 16

**NCERT Exemplar Class 8 Maths Chapter 13 Problem 72**

## If 148101B095 is divisible by 33, find the value of B.

**Summary:**

If 148101B095 is divisible by 33, the value of B = 4

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